## how to find spectral factorization fast?

Started by in comp.dsp15 years ago 2 replies

Hi all, In my recent study, I frequently have to find spectral factoriztion(in the Z-transform form) of a spectrum: for example,...

Hi all, In my recent study, I frequently have to find spectral factoriztion(in the Z-transform form) of a spectrum: for example, Syy(z)=some rational spectrum, need to find Syy_plus(z) and Syy_minus(z), where Syy+(z) is causal and stable... and Syy(z)=Syy_plus(z)*Syy_minus(z) forms a spectrum factorization of Syy(z)... Sometimes this becomes very tedius... can this be done in Matlab...

## how to do bi-lateral Z-transform in Matlab?

Started by in comp.dsp15 years ago 1 reply

Hi all, I wanted to use bi-lateral Z-transform, and esp. I wanted to use Inverse Bilateral Z-transform... But Matlab only provides...

Hi all, I wanted to use bi-lateral Z-transform, and esp. I wanted to use Inverse Bilateral Z-transform... But Matlab only provides Uni-lateral Z-transform and Inverse Transofrm through its "ztrans" and "iztrans" command pair... How to do Bi-lateral Z-transfrom using Matlab? Thanks a lot!

## I thought I knew partial fractions... Help welcome

Started by in comp.dsp14 years ago 13 replies

Here is a very simple Z-transform: z**-1 z**-1 X(z) = ---------------------------- = ------------------------------- ...

Here is a very simple Z-transform: z**-1 z**-1 X(z) = ---------------------------- = ------------------------------- 1 - 0.25 z**-1 - 0.375 z**-2 (1 - 0.75 z**-1)(1 + 0.5 z**-1) Since I have not found a way to use the circumflex to denote ?raised to power?, I used ?**? instead, and I used no symbol to denote multiplication. Whether I use long division or r...

## Who Invented the Z Transform

Started by in comp.dsp14 years ago 34 replies

It's pretty easy to figure out who was responsible for the Fourier transform, ditto for the Laplace. Does anybody out there know who dreamed...

It's pretty easy to figure out who was responsible for the Fourier transform, ditto for the Laplace. Does anybody out there know who dreamed up the z transform (Please tell me it wasn't someone named 'Z')? ------------------------------------------- Tim Wescott Wescott Design Services http://www.wescottdesign.com

## Z transform - choice of z?

Started by in comp.dsp14 years ago 3 replies

> From scratching around on the internet and reading Hamming's Digital Filters book it appears that the z transform is used pretty much...

> From scratching around on the internet and reading Hamming's Digital Filters book it appears that the z transform is used pretty much only with z = exp(iw), which means it works like a discrete Fourier transform. I was wondering whether the z transform is ever used with z = exp(iw+y). This seems to be remarkably useful - I wonder if it is impractical to compute for a given signal, therefo

## Frequency convolution

Started by in comp.dsp14 years ago 1 reply

Hello everyone. I have a question I cant find an answer to: Say you have, X(z) the z transform of a sampled time response...

Hello everyone. I have a question I cant find an answer to: Say you have, X(z) the z transform of a sampled time response x[n], i.e. Z{x[n]} = X(z) Does a Y(z) exist s.t. Z{x[n]^2} = Y(z) and if so, how does it relate to X(z)? If you dont feel challenged enough, try this other one: Does a Y2(z) exist such that: Z{abs(x[n])} = Y2(z)? For the first point I am aware that multip...

## Resampling

Started by in comp.dsp14 years ago 26 replies

Dear, I want to resample a real signal from for instance 1024 -> 1027 samples. I prefer not to do it in the temporal domain, in order to...

Dear, I want to resample a real signal from for instance 1024 -> 1027 samples. I prefer not to do it in the temporal domain, in order to avoid large upsampling and downsampling steps. I have read that one possibility could be zero padding in frequency, but for this example I must use a IDFT and not IFFT to transform the signal to time domain. I have heard something about chirp-z transform, but

## Confusion with magnitude plot of a freg response of a filter, plz help

Started by in comp.dsp14 years ago 2 replies

Dear members: Plz tell me what is the point I am wrong. It is my exam. I have to plot the magnitude of the freq response a Low Pass...

Dear members: Plz tell me what is the point I am wrong. It is my exam. I have to plot the magnitude of the freq response a Low Pass filter: y[n]=1/3*(x[n]+x[n-1]+x[n-2]); I used Z transform and found Y(z)/X(z)=H(z)=1/3*(z^2+z+1)/z^2. So there are two zeros at z1=-1/2 +sqrt(3)/2 and z2=-1/2-sqrt(3)/2, and two double poles at zp=0. I plotted it as follows: the magnitude equal...

## If a z transform has a pole on the unit circle does that signal have a fourier transform?

Started by in comp.dsp14 years ago 1 reply

Hi, If I have been given a z-transform and I know that the z transform has a pole on the unit circle at a certain angle, does it mean that...

Hi, If I have been given a z-transform and I know that the z transform has a pole on the unit circle at a certain angle, does it mean that the fourier transform does not exist at all, because I have read a paper where the author tries to derive the fourier transform from the z transform even when it has a poleon the unit circle. I know if all the poles are inside the unit circle and if the s...

## using z transform for a discrete time filter

Started by in comp.dsp14 years ago 4 replies

hi everyone i'm gonna build a car that moves according to a light, ig the light is getting close the car moves backwards, if the light is going...

hi everyone i'm gonna build a car that moves according to a light, ig the light is getting close the car moves backwards, if the light is going away the car follow it. The speed of the car will depend of the rate of change of the light's intensity. If the light intensity is changing slowly the car will move slow if the light is changing fast the car will move fast. I understand that for the rate ...

## Does every function X(z) have an inverse Z transform?

Started by in comp.dsp13 years ago 4 replies

Hi, Here is the formal question: Is this statement true? For every X(z) there exists a corresponding x(n), such...

Hi, Here is the formal question: Is this statement true? For every X(z) there exists a corresponding x(n), such that Z{x(n)}=X(z) Thank you.

## Does the z transform has the property?

Started by in comp.dsp13 years ago 9 replies

Dear ALl: I have question with the bilateral z transform property, D(x) is the product of Q(x) and C(x) After Ztransform , Z(D(x)) =...

Dear ALl: I have question with the bilateral z transform property, D(x) is the product of Q(x) and C(x) After Ztransform , Z(D(x)) = Z(Q(x))* Z(C(x)) * is the convolution operator. is that property hold ? Thanks bin

Started by in comp.dsp13 years ago 6 replies

Hello I need to convert a lead/lag filter to a z transform function. I'll be using the bilinear method. Question, what equation do I...

Hello I need to convert a lead/lag filter to a z transform function. I'll be using the bilinear method. Question, what equation do I use for prewraping the lead and lag times?? For the other filters i've converted i was prewrapping the frequency and using rads/sec. For the lead/lag filters I only have a time constant input. Transfer function is T1*s + 1 g(s) ----------...

## Z-transform of a truncated sequence?

Started by in comp.dsp13 years ago 1 reply

Hi all, Suppose we are given a function F(z) which is the z-transform of a real sequence with index from 0 to infinity in the time domain,...

Hi all, Suppose we are given a function F(z) which is the z-transform of a real sequence with index from 0 to infinity in the time domain, that's to say, F(z) is the Z-transform of a0, a1, a2, ... all the way down... These a's add up to 1. That's to say: a0+a1+a2+a3+ ... =1. Now suppose I want to truncate the sequence into a finite-length version, and thus create a new sequence, whi...

## Z-Transform(poles, Zeros and ROC)

Started by in comp.dsp13 years ago 14 replies

Hi All, Here is a doubt regarding Z-Transform with respect to poles and zeros. Here is the problem example: x(n) = a^n *...

Hi All, Here is a doubt regarding Z-Transform with respect to poles and zeros. Here is the problem example: x(n) = a^n * u(n) X(z) = (n=0 to n=infinity)SUM x(n) * z^ -n; X(z) = 1 + az^-1+(az^-1)^2 +(az^-1)^3+.....+infinity; .....(eq 1) X(z) = 1/(1-az^-1); provided |az^-1| |z| > |a| ......(eq 2) now X(z) can be written as X(z) = z/(z-a). ......(eq

## z-transform of sin(w*t) - Matlab

Started by in comp.dsp13 years ago 3 replies

Hi, below I have two methods to calculate the frequency response of a z-transformed sine signal. Neither of them gives the correct amplitude...

Hi, below I have two methods to calculate the frequency response of a z-transformed sine signal. Neither of them gives the correct amplitude - why? Thanks, Bmalp function zdemo format compact syms w Ts n z phi t Ts = 1 w = 0.1 phi = 0 vz = simplify(ztrans(sin(w*n*Ts+phi))) if 0 [num,den] = numden(simplify(vz)); num = collect(num,'z') den = collect(den,'...

## Z-transform equation

Started by in comp.dsp13 years ago 3 replies

Hi guys! I've got a pretty big pain in the ass - a course work in DSP. To be honest with you I'm a network engineer and electronics are a bit...

Hi guys! I've got a pretty big pain in the ass - a course work in DSP. To be honest with you I'm a network engineer and electronics are a bit far away from my area of interests, but anyway I have to graduate. I read at least 15 different explanations on the Z-transform and I'm still not sure what I'm doing. Here's what I have: 1) A discrete series: x(0)=0, x(T)=-2.5, x(2T)=-3, x(4T)=1.25, x(5T)...

## Calculate frequency response of Z transform with known frequency bins

Started by in comp.dsp11 years ago 7 replies

Hi all, I've been searching for the best way to do this programmically, but I can't seem to come up with a simple solution. I have a...

Hi all, I've been searching for the best way to do this programmically, but I can't seem to come up with a simple solution. I have a program that calculates filter coefficients correctly based on this z-transform: H(z) = (b0+b1*z^-1+b2*z^-2)/(1+a1*z^-1+a2*z^-2) I want to be able to display the magnitude response of this filter from 20Hz-20kHz at specified frequencies (48pts per octa...

## z transform of a digital filter

Started by in comp.dsp13 years ago 5 replies

hello!! I hope you can help me out. I need to find the Z tansform from a Laplace expresi?n: 5(1-e^-sT)/s(s+1)(s+2) Now, I...

hello!! I hope you can help me out. I need to find the Z tansform from a Laplace expresi?n: 5(1-e^-sT)/s(s+1)(s+2) Now, I know that there is a table to calculate this but I can't find anything on the web, maybe you have one, or you'd know someway to solve this, I really need it, I hope you can help me, thanks!

## reed solomon: z transform vs fourier transform

Started by in comp.dsp13 years ago 2 replies

Hi all, I would like to have your opignon, which transform is better : Z-transform or Fourier transform for implementation of reed...

Hi all, I would like to have your opignon, which transform is better : Z-transform or Fourier transform for implementation of reed solomon codec? if it will be implemented on a DSP processor, what would be the performance? will I get a high speed with Z- transform or Fourier transform ? Thanks