Stability of IIR Filters

Started by Randy Yates in comp.dsp2 years ago 24 replies

Folks, First let me ask this: Does the Fs/2-wide sinc function, interpolating at some fractional sample offset, have a z-transform? I don't...

Folks, First let me ask this: Does the Fs/2-wide sinc function, interpolating at some fractional sample offset, have a z-transform? I don't think so, but I thought I'd verify. Now it can be shown that a fractionally interpolating sinc function can generate an infinite output with bounded input. This is commonly described as an unstable filter. BI does not imply BO. For the class of II...


Looking for old TRW app note "Intro to the Z Transform".

Started by Tom in comp.dsp14 years ago 1 reply

Hi, Years ago I obtained a really good explanation ofhe Z Transform called "introduction to the Z transform and its derivation" by Karwoski....

Hi, Years ago I obtained a really good explanation ofhe Z Transform called "introduction to the Z transform and its derivation" by Karwoski. This was a TRW app note. I have since lost my copy and was amazed to find that I could not find it on the internet. That division of TRW that was responsible for the app note haschanged hands a couple of time and that link is lost, I am sure. Does ...


windowing DFT vs FFT (newbie)

Started by Thomas Magma in comp.dsp14 years ago 1 reply

Hello, I wrote a program in Java that does a DFT on raw 8bit samples stored in memory from a RF ADC (Post processing). This allows me to...

Hello, I wrote a program in Java that does a DFT on raw 8bit samples stored in memory from a RF ADC (Post processing). This allows me to easily adjust the span (zoom) when I'm viewing the spectrum. Works great, but slow as hell. So I'm now trying an FFT with a Chirp Z-Transform so I can zoom in on the desired frequency and look for subtle modulation characteristics. I borrowed this code fr...


Z-Transform - ROC

Started by Murty in comp.dsp14 years ago 1 reply

Hi friends! I got a basic doubt in the theoritical dsp. Hope some one can help me. My actual question is: Consider a sequence...

Hi friends! I got a basic doubt in the theoritical dsp. Hope some one can help me. My actual question is: Consider a sequence x(n) whose z-transform is X(z) and ROC is characterized by Rx. Consider another sequence y(n) with z-transform Y(z) and ROC Ry. Now suppose that Rx and Ry are mutually exclusive that is their intersection region is a null-set. Now if I define h(n) as co...


Question about the z-transform for ARMA modelling

Started by Martin in comp.dsp14 years ago 5 replies

Hello! I have some questions about the z-transform and what to use it for in for example ARMA-filters. I know it is used to find poles and...

Hello! I have some questions about the z-transform and what to use it for in for example ARMA-filters. I know it is used to find poles and zeros, but what else? Consider an ARMA filter: y(t)+a1*y(t-1)+a2*y(t-2)=x(t)+c1*x(t-1)+c2*x(t-2) After z-tranformation it can be written: Y(z)=H(z)*X(z) where ...


ESP article Chirp Z transform questions/problems

Started by bo in comp.dsp14 years ago 4 replies

I read the article and downloaded the code (below). Problem is every compiler I have tried (CodeComposer, gnu, VisualC++) has problems with the...

I read the article and downloaded the code (below). Problem is every compiler I have tried (CodeComposer, gnu, VisualC++) has problems with the notations: double[][] xxxx (I indicate occurrences in the code below with '


what is the z-transform of sinc function?

Started by Joenyim Kim in comp.dsp8 years ago 38 replies

Can anybody tell me what is the z-transform of "sinc" function and what is its region of convergence? Thanks a lot, -Joenyim

Can anybody tell me what is the z-transform of "sinc" function and what is its region of convergence? Thanks a lot, -Joenyim


[Q] How can the chirp-z transform be used in resampling?

Started by One Usenet Poster in comp.dsp11 years ago 6 replies

DSP Gurus: I'm familiar with the classic interpolate-filter-decimate approach to multirate DSP. I've heard that the chirp-z transform can be...

DSP Gurus: I'm familiar with the classic interpolate-filter-decimate approach to multirate DSP. I've heard that the chirp-z transform can be used to resample a signal also. Can anyone provide additional information or references (other than Google search results)? Thanks, OUP


FIR gain

Started by Philip Newman in comp.dsp13 years ago 11 replies

I have an FIR filter with the system equation y[n] = 0.25x[n]+0.5x[n-1]+0.25x[n-2] which gives an impulse response of h = [0.25 0.5...

I have an FIR filter with the system equation y[n] = 0.25x[n]+0.5x[n-1]+0.25x[n-2] which gives an impulse response of h = [0.25 0.5 0.25] without resorting to Z-transform analysis, how can I work out the gain of the filter at DC and at the half nyquist frequency? I think the gain of the filter at DC is the sum of the impulse response, in this case 1. but what about the half-nyquist? ...


Laplace to Z transform for second order lag.

Started by Peter Nachtwey in comp.dsp3 years ago 12 replies

I have a problem with verifying the results for the conversion of a Laplace transform to a z transform. The Laplace transform is in a table and...

I have a problem with verifying the results for the conversion of a Laplace transform to a z transform. The Laplace transform is in a table and is: (b-a)/((s+a)*(s+b)) The z transform for this transfer function is: ( z*(exp(-a*T)-exp(-b*T))/((z-exp(-a*T)*(z-exp(-b*T)) Now let: a=1 b=2 T=.001 Where a and b are the poles and T is the sample interval. When s-> 0 the Laplace transfer


Obtaining inverse z-transform of given expression

Started by Mackan in comp.dsp13 years ago 2 replies

Hi group! I need to determine the impulseresponse for a system with...

Hi group! I need to determine the impulseresponse for a system with the transferfunction $$ H(z)=\frac{1-0.5z^{-1}}{1-z^{-1}+0.5z^{-2}} $$ Knowing that the impulserespone is the inverse z-transform of H I thought this would be no problem. However after performing partialfraction decomposition im unable to locate any known z-transforms (that I can look up in a table), so im kind of stuck...


Question about Z transform of decimation

Started by Jeff in comp.dsp13 years ago 1 reply

Hi, I am learning about digital decimation. The problem is like this: Z-transform of input sequence and filter aree X(z), H(z)...

Hi, I am learning about digital decimation. The problem is like this: Z-transform of input sequence and filter aree X(z), H(z) respectively. After the filter H(z), there is a 2 decimation. From one book talking about decimation, it says the Z-transform of output sequence after decimation is: V(z)=(1/2)*[H(z^(1/2)*X(z^(1/2))+H(-z^(1/2)*X(-z^(1/2))] I have learned Z transform, but no Z tr...


phase angle problems

Started by Steve in comp.dsp13 years ago 2 replies

Hi, I'm having some problems with phase angles, in the context of frequency response of a digital filter from its Z transform. I'm just not...

Hi, I'm having some problems with phase angles, in the context of frequency response of a digital filter from its Z transform. I'm just not "getting it". I've been looking around the 'web for relevant material, but all the stuff I've been finding is beyond this and just assumes that the reader can do this stuff. Say you've got a filter with transfer function: H(z) = z ------...


equivalence between Z-transform and Laplace-Transform

Started by AG in comp.dsp13 years ago 2 replies

Hi all, I am studying a digital phase locked loop. The closed loop filter of this loop has the following Z-Transform : H(z) =...

Hi all, I am studying a digital phase locked loop. The closed loop filter of this loop has the following Z-Transform : H(z) = ((K1+K2)*z^-1 - K1*z^-2) / (1 + (K1+K2-2)*z^-1 + (1-K1)*z^-2) I would like to know the damping factor and the natural pulse of the equivalent time continuous filter H(p). by equivalent, I mean a filter H(p) that would give in the time domain, the same resp...


Re: equivalence between Z-transform and Laplace-Transform

Started by Tim Wescott in comp.dsp13 years ago

AG wrote: > Hi Tim, -- snip -- > > > The term "damping ratio" is much more slippery when you're talking > > about discrete-time...

AG wrote: > Hi Tim, -- snip -- > > > The term "damping ratio" is much more slippery when you're talking > > about discrete-time systems. Assuming that I'm not messing up the > > math, if you find the pole locations of your transfer function, z_0 = > > e^{jw + q) then the "damping ratio" is > > > > zeta = q / sqrt(w^2 + q^2). > > What I finally discovered in reading books, is that


How to get the inverse Z-transform of the following expression?

Started by in comp.dsp13 years ago 3 replies

1 H(Z) = --------------------------------- ( 1+0.81*Z^(-2) )( 1+0.81Z^(2) ) So far, only could I get is the...

1 H(Z) = --------------------------------- ( 1+0.81*Z^(-2) )( 1+0.81Z^(2) ) So far, only could I get is the inverse of 1 H1(Z) = -------------------- ( 1+0.81*Z^(-2) ) or 1 H2(Z) = -------------------- ( 1+0.81*Z^(2) ) Any ideas? thanks.


Shameless Plug

Started by Tim Wescott in comp.dsp13 years ago 67 replies

I will be presenting two topics at the 2005 Embedded Systems Conference San Francisco next March -- see http://www.esconline.com/sf/ for show...

I will be presenting two topics at the 2005 Embedded Systems Conference San Francisco next March -- see http://www.esconline.com/sf/ for show details. "Basic Control Theory for the Software Engineer" is as much information on the z-transform as I can fit into 90 minutes. It gives a high-altitude overview of designing software control loops in a systematic manner. "PID Without a Ph...


DFT z-transform help needed

Started by Anonymous in comp.dsp13 years ago 13 replies

Hi, I have the following questions that I am stuck on. Could you please help in solving them or at least point me in the direction that can help...

Hi, I have the following questions that I am stuck on. Could you please help in solving them or at least point me in the direction that can help me? Thanks. A given sequence x has x[n]=0 for n outside the range 0


Simple z-transform question

Started by ?ine Canby in comp.dsp13 years ago 3 replies

Hi, The transfer function for a lossy integrater is H(z) = z/(z-c) the magnitude spectrum is given by M(f) = |z|/|z-c| so lets...

Hi, The transfer function for a lossy integrater is H(z) = z/(z-c) the magnitude spectrum is given by M(f) = |z|/|z-c| so lets say I have a c value of 0.8, how do I plot M(f)? I simply tried plugging in values for z ni the range of 0 to 1, but this does not give me what I would expect and I think I'm totally misunderstanding the z transorm. Any help?


Z-transform: Final Value theorem

Started by Ajay in comp.dsp12 years ago 15 replies

Hi, I have encountered a strange conceptual problem while calculating value of sequence x(n) at Inf. the function x(n) is defined as x(n)...

Hi, I have encountered a strange conceptual problem while calculating value of sequence x(n) at Inf. the function x(n) is defined as x(n) = 1 when n is even 0 otherwise. I calculated z-transform of x(n) to be X(z) = 1/(z^2 -1); ROC : |z| = 1; -- (1) Query1 : Have I calculated the transform correctly? Transfrom seems to exist only on the unit circle. Now, In order to ca...