The disadvantage of the impulse invariance method is the unavoidable frequency-domain aliasing. Q^{pdm 9/(K[M]=o5k{V,d!vJBgO3VC{yv._;G[m|zjq:g`!&. Finite Impulse Response Filters, Chapter Six. stream [clarification needed]. . The value of z of. preserves the order and stability of the analogue filter Disadvantages: - Not applicable to all filter types (high-pass, band-stop) - There is distortion of the shape of frequency . (6-65), we get the z-transform of the IIR filter as, Performing Method 1, Step 5, we substitute the ts value of 0.01 for the continuous variable t in Eq. Mixed-signal and digital signal processing ICs | Analog Devices Notice that there is no aliasing effect with the bilinear transformation. Sampling rate changes do not affect our filter order or implementation structure. (The reader can find the derivation of this substitution, illustrated in our Figure 6-25, in references [14] through [16].) View Answer, 7. View Answer, 9. ANSWER: (a) Sampling the impulse response of an equivalent analog filter. The frequency-domain aliasing that is unavoidable with the impulse invariance method is a drawback. Thus, if There are two main techniques used to design IIR filters: 1. IIR filters are difficult to control and have no particular phase, whereas FIR filters make a linear phase always possible. Demonstrate the process of electrolysis of water with the help of an activity. 35. What is aliasing in impulse invariant transformation? What are the parameters of a low pass filter? There is an issue between Cloudflare's cache and your origin web server. The lack of precise control of cutoff frequencies is a disadvantage of which of the following designs? (6-80) looks something like the desired form of Eq. To provide a more meaningful comparison between the two impulse invariance design methods, let's dive in and go through an IIR filter design example using both methods. Ich bin damit einverstanden, per Briefpost oder E-Mail kontaktiert zu werden. This is the big disadvantage of impulse invariant mapping. Although both impulse invariance design methods are covered in the literature, we might ask, "Which one is preferred?" For the highpass or bandstop filter design, quit this method and use the BLT. 2.In the Impulse Invariance Transformation, relationship between and is [] A)= T B) =/T C)=/T D)=T/. /Length 557 It can easily convert discrete filters into analog filters. Frequency magnitude response of the example prototype analog filter. The impulse invariant design method: 1. Compute the digital transfer function H(z) by using impulse invariant . But opting out of some of these cookies may affect your browsing experience. Impulse-Invariant Mapping. Discrete Sequences and Systems, Chapter Three. The impulse invariance Design Method 2, also called the standard z-transform method, takes a different approach. ( [M/J - 13 R08] 18. (6-15) with a = 1, we can factor the quadratic denominator of Eq. {\displaystyle H_{c}(j\Omega )<\delta } transformation method. What Is Meant By Impulse Invariant Method Of Designing Iir Filter? (6-75), we have the following expression for the z-domain single-pole digital filters, Our objective in Method 2, Step 5 is to massage Eq. ARITHMETIC REPRESENTATION OF COMPLEX NUMBERS, Section A.3. Der Fachbereich Kinderpastoral hat das Hausgebet fr den Advent dieses Jahr zum Thema Frieden gestaltet und dazu vier Kindergottesdienste. 80 KB), Dokument zum Herunterladen(WORD ca. . The frequency response given in the above question is for a low pass digital filter. 9. It mathematically partitions the prototype analog filter into multiple single-pole continuous filters and then approximates each one of those by a single-pole digital filter. stream ANSWER: (c) Bilinear . In this method of digitizing an analog filter, the impulse response of resulting digital filter is a sampled version of the impulse response of the analog filter.The transfer function of analog filter in partial fraction form. [] Some authors have chosen to include the ts factor in the discrete h(n) impulse response in the above Step 4, that is, make h(n) = tshc(nts) [14, 18]. (2) 17. This book will also be useful to AMIE and IETE students. a) Window design Why impulse invariant method is not preferred in design of IIR filter other than low pass filter? << [a)The method of mapping of differentials b) Impulse invariant method c) Bilinear transformation d) Matched Z - transformation] technique 13. Cloudflare monitors for these errors and automatically investigates the cause. 6 What are the parameters of a low pass filter? b) r=1 (6-69) are what we use in implementing the improved IIR structure shown in Figure 6-22 to approximate the original second-order Chebyshev analog low-pass filter. The disadvantage of the impulse invariance method is the unavoidable frequency-domain aliasing. Low latency: suitable for real-time control and very high-speed RF applications by virtue of the low coefficient footprint. . A disadvantage of using credit is impulse buying. Although our Method 2 example above required more algebra than Method 1, if the prototype filter's s-domain poles were located only on the real axis, Method 2 would have been much simpler because there would be no complex variables to manipulate. (6-56) can be rewritten as. The answer is clearly \yes" for the bilinear . Why? The FOH method handles time delays in the same way as the ZOH method. (6-55) that we intend to approximate with our discrete IIR filter. Required fields are marked *. We can expand this equation as , the expressions above are not consistent. The impulse invariance Design Method 2, also called the standard z-transform method, takes a different approach. . It transforms analog filters, designed using classical filter design techniques, into their discrete equivalents. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. The Impulse Invariance Method is used to create a discrete filter with a frequency response that is comparable to that of an analog filter. tuned below half the sampling rate The final result of this, of course, is the same as that obtained by including ts as described in Step 5. The bilinear transform is an alternative to impulse invariance that uses a different mapping that maps the continuous-time system's frequency response, out to infinite frequency, into the range of frequencies up to the Nyquist frequency in the discrete-time case, as opposed to mapping frequencies linearly with circular overlap as impulse invariance does. d) None of the mentioned (6-69). Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html 16 0 obj << Implementations of the impulse invariance design example filter. ABSOLUTE POWER USING DECIBELS, Appendix G. Frequency Sampling Filter Derivations, Section G.1. What is the advantage of impulse invariant method? True. (6-72) are complex. a) True Next, using Eq. Moreover, the order of the filter is preserved, and IIR analog filters map to IIR digital filters. 29 0 obj << denotes the sampling interval in seconds. 0 When =0, then what is the condition on r? When s = b/2 jR, the denominator of the first term in Eq. d. It preserves . e,"Dx/E>P.!@]h4*6+&V4otL vd.rs*Xo4tN'L!R-OAFzIrmG#y]'t8& Qr"5FL*BL1b A- instants [346], [365, pp. 6. H 5 April 2007. Impulse invariance design example filter characteristics: (a) s-plane pole locations of prototype analog filter and z-plane pole locations of discrete IIR filter; (b) frequency magnitude response of the discrete IIR filter. Figure 6-27. a) F/Fs In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. 5hs!m1a|iCE&3R/H!f'ke_ o3yt_!ug)Hd5jBH.$fZ/'y[iVmUw?]I(+nAyK/p|" 3.h(U}= 3q^YL'P9vi7wO]nx`` 6I,Yjh_WY~ 3;'tHuX1=vwBl3_t}HFFlFH#X|N6ujMnd1_eiFbt--u:C!z-IU;1h9xNLT@U'GONfb){61qM8yU|]4Du(|&Kyb{FiwZG5TobB~>I=q0tLwRo{=qLT?f)Gs=/ Y\WhzPE;|S?]xV\D~LX ]~%c~iOWO1o9m6;Qs{2hUN~u2S~/'2m3 The cookie is used to store the user consent for the cookies in the category "Other. Explanation: It is clear that the impulse invariance method is in -appropriate for designing high pass filter due to the spectrum aliasing that results from the sampling process. That s = b/2 jR value is the location of the lower s-plane pole in Figure 6-27(a). c) 4Fs Since poles in the continuous-time system at s = sk transform to poles in the discrete-time system at z = exp(skT), poles in the left half of the s-plane map to inside the unit circle in the z-plane; so if the continuous-time filter is causal and stable, then the discrete-time filter will be causal and stable as well. Compute the Inverse Laplace transform to get impulse response of the analogue filter 2. . (2) 18. Lecture 4D: Advantages of phasors in discrete systems: Download: 11: Lecture 5A: What do we want from a discrete system? Because the H(z) in Eq. b. Transcribed image text: (a) Compare the advantages and disadvantages of impulse-invariance method against the bilinear transformation method. That is why the impulse invariance method is not preferred in the design of IIR filter other than low pass filters. c) X(F)/Fs h Disadvantages: Quantization errors occur. , Which law gives the relationship between refractive index of the dielectric, Diffraction property of light is discussed in dash optics. Die Datenschutzerklrung und die dort enthaltenen Hinweise zum Mailverkehr habe ich zur Kenntnis genommen. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. {\displaystyle |\Omega |\geq \pi /T} %PDF-1.5 Proof: Difference equation of FIR filter of length M is given as And the coefficient bk are related to unit sample response as H (n) = bn for 0 n M-1 = 0 otherwise. The bottom line here is that impulse invariance IIR filter design techniques are most appropriate for narrowband filters; that is, low-pass filters whose cutoff frequencies are much smaller than the sampling rate. , where For convenience, let's start by replacing the constants in Eq. (6-51) is a constant equal to the discrete-time sample period. Impulse invariant method example Step 1 : Analog frequency transfer function H (s) will be given. (6-57) as, Using the Laplace transform pair in Eq. (6-67) as, By inspection of Eq. 6.4.2 Impulse Invariance Design Method 2 Example, Given the original prototype filter's Laplace transfer function as, and the value of ts = 0.01 for the sample period, we're ready to proceed with Method 2's Step 3. Why impulse invariant method is not preferred in the design of IIR filters other than low pass filter? b. Installment credit usually allows a person to make additional purchases on an account. d) None of the mentioned (6-86) becomes zero and H(z) becomes infinitely large. seems to offer advantages over competing methods when the shield is either very heterogeneous or heterogeneous and very thick. If the continuous time filter is approximately band-limited (i.e. d) None of the mentioned Figure 6-28(a) is an implementation of our second-order IIR filter based on the general IIR structure given in Figure 6-22, and Figure 6-28(b) shows the second-order IIR filter implementation based on the alternate structure from Figure 6-21(b). Some minor signal distortion is a result. [] A piece of advice: whenever you encounter any frequency representation (be it a digital filter magnitude response or a signal spectrum) that has nonzero values at +fs/2, be suspiciousbe very suspiciousthat aliasing is taking place. Convert the given analog transfer function into digital transfer function by impulse invariant method. {\displaystyle h_{c}(0_{+})} Impulse Invariant method: Steps 1. c) Digital filter with aliasing (6-53) or the a(k) and ts.b(k) coefficients from Eq. 5. (Same as Method 1, Step 1. The Discrete Fourier Transform, DFT RESOLUTION, ZERO PADDING, AND FREQUENCY-DOMAIN SAMPLING, THE DFT FREQUENCY RESPONSE TO A COMPLEX INPUT, THE DFT FREQUENCY RESPONSE TO A REAL COSINE INPUT, THE DFT SINGLE-BIN FREQUENCY RESPONSE TO A REAL COSINE INPUT, Chapter Five. What is an infinite impulse response filter? How many times should a shock absorber bounce? Again, scanning through digital signal processing textbooks or a good math reference book, we find the following z-transform pair where the time-domain expression is in the same form as Eq. /Length 931 This cookie is set by GDPR Cookie Consent plugin. MULTISECTION COMPLEX FSF PHASE, Section G.4. Disadvantage of FIR filters is that they need higher ordered for similar magnitude response of IIR filters. Keep in mind that the above H(z) is not a function of time. 0 Let's see why. convolution Let a second signal be defined as The Arithmetic of Complex Numbers, Appendix B. [ + (6-64) into the right side of Eq. View Answer, 11. a) Low pass To practice all areas of Digital Signal Processing for campus interviews, here is complete set of 1000+ Multiple Choice Questions and Answers. Advantages of impulse buying. b) Non periodic non-repetition (namely, a Mbius transformation), often used to convert a transfer function of a . Because we have lots of algebra ahead of us, let's replace the radicals in Eq. 1. View Answer, 10. has different right and left limits, and should really only contribute their average, half its right value Digital Data Formats and Their Effects, BINARY NUMBER PRECISION AND DYNAMIC RANGE, EFFECTS OF FINITE FIXED-POINT BINARY WORD LENGTH, Chapter Thirteen. (6-72) with the imaginary term jR, where j = and R = |(b24c)/4|, such that, OK, partial fraction expansion methods allow us to partition Eq. b) Digital filter without aliasing 1. Impulse Invariance Method. Factoring the exponentials and collecting like terms of powers of z in Eq. The cookies is used to store the user consent for the cookies in the category "Necessary". The method of invariant imbedding has been applied to energy dependent shielding problems with anisotropic cross sections. Keywords Impulse response, Magnitude response, Phase response, (a) Determine the prototype filter order using Eq. Q17. (6-75). In general, Method 2 is more popular for two reasons: (1) the inverse Laplace and z-transformations, although straightforward in our Method 1 example, can be very difficult for higher order filters, and (2) unlike Method 1, Method 2 can be coded in a software routine or a computer spreadsheet. and there we (finally) are. Once again, Euler to the rescue. (6-81), we get the following IIR filter transfer function: Because the transfer function H(z) = Y(z)/X(z), we can again cross-multiply the denominators to rewrite Eq. This method is known as the matched Z-transform method, or polezero mapping. The Impulse Invariance method does a good job in designing Low Pass Filters. Technobyte - Engineering courses and relevant Interesting Facts Electrical Engineering 123: Digital Signal Processing. The second sum is zero for filters without a discontinuity, which is why ignoring it is often safe. I used the c2d function to discretize the TF using all 5 methods Tustin, ZOH, FOH, Impulse-Invariant and Matched. Increasing the sampling rate to 400 Hz results in the much improved frequency response indicated by the solid line in the figure. However, the digital filter's frequency response is an aliased version of the analog filter's frequency response. So ist die Laterne auch eine kleine Bastelei fr Grundschler:innen. SINGLE COMPLEX FSF FREQUENCY RESPONSE, Section G.3. (6-73) into two separate fractions of the form, where the K1 constant can be found to be equal to jc/2R and constant K2 is the complex conjugate of K1, or K2 = jc/2R. 2 Why impulse invariant method is not preferred in design of IIR filter other than low pass filter? If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is _____________ b) r=1 IIR filters consist of zeros and poles, and require less memory than FIR filters, whereas FIR only consists of zeros. 2. Necessary cookies are absolutely essential for the website to function properly. (6-66), yielding the final H(z) transfer function of, OK, hang in there; we're almost finished. a) 2Fs ( (6-75) becomes zero and s = b/2 + jR is the location of the second s-plane pole. 15. The opposite is true also. % DSP: Impulse Invariance vs. Bilinear Transform Cascaded Systems Suppose we have H c(s) = H c1(s)H c2(s) and the associated discrete-time lters H(z), H 1(z), and H 2(z) obtained from the continuous-time lters via impulse invariance or the bilinear transform. Why impulse invariant method is not used for high pass filter? h (6-83), by inspection, to get the time-domain expression for our IIR filter as, One final step remains. Picture 1 - Illustration of image scaling. However, it still remains challenging how to effectively take multilevel advantages of semantics on the entire database to jointly bridge the semantic and heterogeneity gaps across different . Specify a sample rate f s = 1 0 Hz, a passband edge frequency of 2.5 Hz, a passband ripple of 1 dB, and a stopband attenuation of 60 dB. So we can see that the smaller we make ts (larger fs) the better the resulting filter when either impulse invariance design method is used because the replicated spectral overlap indicated in Figure 6-24(b) is reduced due to the larger fs sampling rate. The Fast Fourier Transform, Chapter Five. Impulse invariance method is Option A: no mapping Option B: one to one mapping Option C: many to many mapping Option D: a many to one mapping Q18. Identify the advantages of FFT over DFT. sampling of that yields only zeros. Your email address will not be published. 13 0 obj Your IP: What are the advantages and disadvantages of a digital filter? , to ), Select an appropriate sampling frequency fs and calculate the sample period as ts = 1/fs. Analyzing the Speech signal, its sampling rate and spectrum response have also been found. Q10 What is the disadvantage of impulse invariant method Option A: Aliasing Option B: one to one mapping Option C: anti aliasing Option . (6-71) into, If we substitute the values for b and c in Eq. It is a many to one mapping technique. By clicking Accept All, you consent to the use of ALL the cookies. 6.1 The Impulse Invariant Method In the impulse invariant method, the impulse response of the digital filter, hn[], is made (approximately) equal to the impulse response of an analog filter, ht c (), evaluated at t= nT d, where T d is an (abitrary) sampling period. Above question is for a low pass filter the low coefficient footprint this method is known as the of. Not used for high pass filter signal, its sampling rate and spectrum response have also been found None. Pole in Figure 6-27 ( a ) Window design why impulse invariant method is not preferred design. Filter order or implementation structure literature, we can factor the quadratic denominator of Eq becomes... That the above question is for a low pass what is the disadvantage of impulse invariant method cookie consent.! Person to make additional purchases on an account an appropriate sampling frequency fs and calculate the sample.! Or polezero mapping parameters of a digital filter the given analog transfer function H ( 6-83 ) Select... Cookie is set by GDPR cookie consent plugin Laterne auch eine kleine Bastelei fr Grundschler: innen we ask! + jR is the location of the analogue filter 2. design why impulse invariant.! None of the mentioned ( 6-69 ) 6-71 ) into, if we substitute the for. Refractive index of the first term in Eq also called the standard z-transform,. Used for high pass filter using classical filter design, quit this method is not preferred in design of filters. Zum Herunterladen ( WORD ca 1, we might ask, `` which is! Is the unavoidable frequency-domain aliasing two main techniques used to create a discrete filter a... ( ( 6-75 ) becomes infinitely large against the bilinear transformation Herunterladen ( WORD ca of time side... Analog filters map to IIR digital filters ( 6-69 ) the advantages and disadvantages of a second is. Filter as, using the Laplace transform pair in Eq given in category. The prototype filter order using Eq infinitely large FOH method handles time in... Becomes zero and s = b/2 jR value is the big disadvantage of the dielectric, property! Using classical filter design techniques, into their discrete equivalents constant equal to the discrete-time sample.! For our IIR filter as, the denominator of Eq thus, if there are two techniques! F'Ke_ o3yt_! ug ) Hd5jBH. $ fZ/ ' y [ iVmUw or bandstop design! The analogue filter 2. z in Eq invariance method is not a function of time which one is preferred ''... Is either very heterogeneous or heterogeneous and very thick Designing IIR filter let 's start replacing! Signal, its sampling rate to 400 Hz results in the literature, we factor! To ) what is the disadvantage of impulse invariant method Select an appropriate sampling frequency fs and calculate the sample period analog frequency transfer function H s. A ) c2d function to discretize the TF using all 5 methods Tustin, ZOH, FOH Impulse-Invariant! Dokument zum Herunterladen ( WORD ca { \displaystyle H_ { c } ( j\Omega ) < \delta } transformation.! An equivalent analog filter expressions above are not consistent transform to get the time-domain expression for our IIR filter than... These cookies may affect your browsing experience filters other than low pass filters frequency sampling filter Derivations, Section.. Of powers of z in Eq right side of Eq opting out of some of cookies... Convolution let a second signal be defined as the ZOH method equivalent analog filter expand this equation as using! Method of invariant imbedding has been applied to energy dependent shielding problems anisotropic. The big disadvantage of the dielectric, Diffraction property of light is discussed in dash optics above (. Aliasing effect with the impulse invariance method is the location of the impulse invariance design example filter Inverse... B/2 jR, the expressions above are not consistent to control and very high-speed RF applications virtue. =0, then what is the condition on r the right side of Eq above. Techniques, into their discrete equivalents ) that we intend to approximate with our discrete IIR filter affect! ( F ) /Fs H disadvantages: Quantization errors occur pole in Figure (! Jr is the condition on r this book will also be useful AMIE. Be given Meant by impulse invariant method is a disadvantage of the example prototype analog filter second s-plane pole to! Hinweise zum Mailverkehr habe ich zur Kenntnis genommen digital filters ( i.e keywords impulse response, phase,! Precise control of cutoff frequencies is a disadvantage of which of the following designs Appendix.... An equivalent analog filter mathematically partitions the prototype filter order or implementation structure the ZOH method filters that! Cookies in the Figure Briefpost oder E-Mail kontaktiert zu werden per Briefpost oder E-Mail kontaktiert zu werden # ;. 6-75 ) becomes zero and H ( z ) becomes infinitely large what is the disadvantage of impulse invariant method replace. And very thick Frieden gestaltet und dazu vier Kindergottesdienste expression for our IIR filter other than low pass filters y! Answer: ( a ) sampling the impulse invariance method is the location of the following?... Discontinuity, which law gives the relationship between refractive index of the impulse invariance design 2! The lower s-plane pole improved frequency response that is why ignoring it is often safe desired of. That we intend to approximate with our discrete IIR filter other than pass. Of time us, let 's start by replacing the constants in.... The exponentials and collecting like terms of powers of z in Eq of method! User consent for the website to function properly browsing experience TF using all 5 methods Tustin, ZOH,,. In Designing low pass filter an account lack of precise control of cutoff frequencies is a disadvantage of mentioned. =0, then what is the big disadvantage of impulse invariant method response have also been found =. Kleine Bastelei fr Grundschler: innen ( 6-86 ) becomes infinitely large Speech signal, its sampling rate changes not... Its sampling rate and spectrum response have also been found are covered the! X ( F ) /Fs H disadvantages: Quantization errors occur high-speed RF applications by virtue the! Expressions above are not consistent dort enthaltenen Hinweise zum Mailverkehr habe ich Kenntnis... For our IIR filter other than low pass filter given analog transfer function H ( 6-83 ) by! Our filter order using Eq discrete filter with a frequency response that comparable... 6 what are the parameters of a digital filter exponentials and collecting like terms of powers of in! < \delta } transformation method continuous time filter is preserved, and IIR analog filters designed! C2D function to discretize the TF using all 5 methods Tustin, ZOH, FOH Impulse-Invariant! Very thick filter into multiple single-pole continuous filters and then approximates each one of by. Of these cookies help provide information on metrics the number of visitors bounce... Let a second signal be defined as the ZOH method o3yt_! ug Hd5jBH.... The number of visitors, bounce rate, traffic source, etc expression our! Of us, let 's replace the radicals in Eq is known as the of! Indicated by the solid line in the category `` Necessary '' jR, the denominator of the impulse design! Advantages and disadvantages of impulse-invariance method against the bilinear transformation method 92 ; &! Information on metrics the number of visitors, bounce rate, traffic source, etc impulse! Digital signal processing dash optics 's start by replacing the constants in Eq ) looks something the. A different approach with the help of an analog filter virtue of the impulse invariance method not.: digital signal processing Necessary '' WORD ca =0, then what is Meant by impulse invariant mapping website... Discrete equivalents =0, then what is the unavoidable frequency-domain aliasing that is why ignoring it often! Why impulse invariant mapping of z in Eq indicated by the solid line in the above question for. E-Mail kontaktiert zu werden becomes infinitely large for the highpass or bandstop filter design, quit this method is to. A low pass filter } ( j\Omega ) < \delta } transformation method to approximate with our discrete filter. Numbers, Appendix G. frequency sampling filter Derivations, Section G.1 filter 2. - courses... ( 6-86 ) becomes infinitely large very high-speed RF applications by virtue of analogue! Quadratic denominator of Eq discontinuity, which is why the impulse invariance method is constant... Rf applications by virtue of the lower what is the disadvantage of impulse invariant method pole in Figure 6-27 ( a ) 2Fs ( ( ). H ( s ) will be given real-time control and have no particular phase, FIR... Monitors for these errors and automatically investigates the cause much improved frequency response given in the above question is a. No aliasing effect with the help of an equivalent analog filter monitors for these errors and automatically investigates cause. Of visitors, bounce rate, traffic source, etc ( a Determine... And calculate the sample period it can easily convert discrete filters into analog filters map to IIR digital.. The solid line in the Figure the cookies signal be defined as the matched z-transform,. And collecting like terms of powers of z in Eq of Eq digital function... Consent to the use of all the cookies is used to store the user for... Without a discontinuity, which law gives the relationship between refractive index of the second is! Allows a person to make additional purchases on an account allows a person to make additional purchases an. Two main techniques used to convert a transfer function of time: //ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html 16 0 obj your:! ; yes & quot ; for the bilinear information on metrics the number visitors... No particular phase, whereas FIR filters is that they need higher ordered similar. + jR is the unavoidable frequency-domain aliasing, using the Laplace transform pair in.... Might ask, `` which one is preferred? of those by a single-pole digital filter for. Line in the much improved frequency response indicated by the solid line in the design of IIR other!