# Questions tagged [z-transform]

The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.

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### Digtial FIR Impulse response & transfer function

I am currently working the figure through below. as it is an FIR Filter i have worked out using convolution that the output is 4,2,4,6,0,0. i am trying to obtain the 'z' domain transfer function of ...
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### How would one solve this question if no initial conditions are given? Which assumption can I make?

This was a question on our test, I know it can be easily solved by Z-transforms but there are no initial conditions specified. In this case, what would be the right approach? Assume all initial ...
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### Why not use a complex number in the exponent in the z-transform?

I am trying to comprehend how the z-transform has come to be similar but different from its continuous counterpart, namely the Laplace transform. It seems to me that the most parallel and intuitive ...
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### Z Transform of M-Fold Decimation

I know this is probably a common question, but after some searching I think that my version of the question is slightly different -- apologies if this is a repeat. I have seen that it is inaccurate to ...
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### Poles and Zeros of a DiscreteTimeModelFunction with delay in Wolfram Mathematica

help me please, I have a problem with this TransferFunctionModel, When I want to obtain the poles from the Discrete Model Wolfram gives me an error, what am I doing wrong? Could it be the delay of the ...
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### Find Fourier Transform of Unit Step using the $z$-Transform [duplicate]

Since the unit step $u[t]$ is not absolutely summable, it has no Fourier Transform. In the DSP book (Proakis), the Fourier Transform of the unit step is formed by evaluating its $z$-Transform on the ...
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### Discrete Filter $y[n] = \frac{1}{3} x[n] + \frac{1}{3} x[n-1] + \frac{1}{3} x[n-2]$

Consider the filter which equation can be represented by $y[n] = \frac{1}{3}x[n] + \frac{1}{3}x[n-1] + \frac{1}{3}x[n-2]$, in $x[n]$ and $y[n]$ are sequence of input and output of the system ...
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### Inverse z-transform. Where is mistake?

I've already wrote about that trouble (link here), but I don't understand where I've made a mistake. Full description of the task is as follows: Z-transform of sequence {x(k)} describe by the ...
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### Summations in Z-Transform

I'm currently working on a problem that involves a Z-Transform. Basically, the essence of the problem is that if: $$H\left(z\right) = \sum_{n=0}^{N-1}h\left(n\right)z^{-n}$$...
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### Z transforms doubt -(ROC and its purpose)!

i had this doubt previously queried in another forum, but unfortunately had no answer. Consider a signal 3^n u[n]. Take its Z transform, which is Z/(Z-3). Now i know that in real sense, Z is a delay ...
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### Determine transfer function based on a diagram with ai coefficients given

From a diagram with input $x(n)$ a summer and three feedback delay taps I get the difference equation... $$y(n) = x(n)+a_1y(n-1)+a_2y(n-2)+a_3y(n-3)$$ Then I am given values for ai coefficients. Case1:...
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### Design discrete controller for zero steady state error

I have the following system where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ...
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### How do I represent any signal in the form x[n]u[n] and x[n]u[-n-1]?

For eg-: If I have the signal x[n]={1,a,a²...}I can represent it as a^n * u[n]. Similarly if I havethe sequence as x[-1]=-a^-1 x[-2]=-a^-2 Then I can represent it as x[n]=-a^n*u[-n-1].
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### DSP: newbie not understanding z transform/complex sinusoidal frequency and phase

Im reading Will Pirkles Designing audio effect plugins book and I'm not sure if I'm understanding the z transform correctly. I got up to differential equations in college, but haven't done math in ...
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### How to find the difference equation directly from Direct Form II signal flow graph

I am trying to solve for the difference equation of the following signal flow graph: I am aware that Direct Form II can be converted to Direct Form I, which finding the difference equation directly ...
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### Polar Fourier Transform and its similarity to the Z-Transform

The DFT is given by $X_{\mathcal{F}}(k) = \sum_{n=0}^{N-1} x_n e^{-j 2 \pi k n / N}$ Knowing that complex numbers can also be represented using a polar form $A \angle\theta$, I was looking for a ...
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### Having trouble interpreting z-transform description of a predictor from a codec paper

I've been looking at the opus paper (https://arxiv.org/pdf/1602.04845.pdf); in particular, in section 4.1, they describe the predictor for the current band energy based on energy from both the current ...
Given a high pass transfer fn of the form $H_{hp}=a_{1}*z^0 +a_{2}*z^{-1} + ... a_{n}*z^{-n}$ Is it possible to calculate a causal low pass filter using $H_{lp} = z*(1-H_{hp})$ ? attempting $H_{... 1answer 34 views ### Mixed - Discrete and Continuous system Laplace domain stability - Effect of Sampler and DAC I have a system whose the plant transfer function is continuous and the compensation is discrete. I have an ADC which allows to measure the output of the system and a DAC which allows to control the ... 1answer 42 views ### Identify out signal from in signal and impulse response Hi there I am studying a course in signal processing and systems. I was given an excecise which I am having a great deal of trouble solving. I am allowed to solved using matlab, but for top marks I ... 1answer 51 views ### Zeros and poles from transfer function I have a transfer function $$H(z) = \frac{Y(z)}{X(z)} = 1 - 0.5z^{-1} \text{.}$$ I'm interested in zeros and poles. I know I need to adjust the function to $$H(z) = \frac{\prod_i(z-n_i)}{\prod_i(z-... 2answers 142 views ### Difference equation to FIR filter coefficients I have a difference equation$$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ... 0answers 20 views ### Z-transform of a multilinear function/ consecutive multplication of k signals y_1(n), \ldots, y_k(n) How should one go about calculating the Z-transform of a signal that is the multiplication of k signals (i.e. a multilinear function with regards to signals y_1(n) \ldots y_k(n) ? Namely, \... 1answer 33 views ### inverse z transform performed on 6th order IIR filter we are told to find coefficients and impulse response of IIR filter of order of 6. There are 6 zeros and 6 poles in the design. Pole and zero pairs are conjugate and poles are within the unit circle ... 1answer 79 views ### If we take Z-transform of a signal & find its ROC. How to use this ROC? There are ∞ signals in ROC, suppose we choose any signal what to do with it? If we take Z-transform of a signal & find its ROC. How to use this ROC? There are infinite signals in ROC, suppose we choose any signal from ROC, what to do with it? 0answers 20 views ### Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically with the signals in ROC? Suppose a signal is growing exponentially. We take its Z transform & find its ROC. So what are we supposed to do practically? Are we supposed to manipulate our O/P by multiplying any signal from ... 1answer 38 views ### I tried two approaches and gained the different conclusions of judging the stability of the transfer function of the system We want to judge whether the system is stable or not. Given the below transfer function.$$ H\left( z \right) =\frac{\left( 1+2 z^{-1} \right) }{\left( 2+z^{-1} \right) }  H\left( z \right) ... 3answers 384 views ### Filter odd or even harmonics with notch or inverse notch filter Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ... 0answers 65 views ### Let a LTI system be causal and stable with the transfer function being... show that if the system is an IIR LTI causal and stable one, and the transfer function is $H(z)=\sum_{n=0}^{\infty}h[n]z{^{n}}= \frac{G}{1 -\sum_{k=1}^{p}a_kz{^{-k}}}$ show that the cepstrum of this system ... 2answers 198 views ### Where to start with DSP? I have a DSP exam coming up this summer and I got an abysmal mark on an assignment earlier this year. Obviously, the lecture slides are not enough for me to understand DSP, so I am wondering where can ... 1answer 52 views ### Power Spectral Density of a Filter I need to calculate the output power spectral density of the following digital filter My calculations are as follows:$y\left(n\right)\:=\:x\left(n-1\right)+d\left[x\left(n-1\right)+x\left(n\right)\...
I have the following system: $$y[n]=\frac{1}{3}(x[n+1]+x[n]+x[n-1])$$ After the Z-Transform we get $$\frac{y[z]}{x[z]}=\frac{z^2+z+1}{3z}$$ which is of course the transfer function of the system. ...