# 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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### 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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### 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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### Value of $\sum\limits_{n=-\infty}^{\infty}(x*x)[n]$

If $x[n]=(0.5)^nu[n]$ and $y[n]=(x*x)[n]$ then what is the value of $\sum\limits_{n=-\infty}^{\infty}y[n]$ ? I calculated the $\mathcal{Z}$-transform of $x[n]$ and then applied the accumulation ...
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### Z-transform of $\cos(\omega_0 n(n+1))u[n]$

I'm doing some research on Zadoff-Chu sequences and as a part of it I wanted to find the Z-transform of: $$\cos(\omega_0 n(n+1))u[n]$$ Wolfram Alpha / Mathematica couldn't help out. I couldn't find a ...
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How would one go about calculating the Magnitude of... $\mathcal{Z}$-transform = $$\frac{1}{1-z^{-2}}$$ I understand that z can be replaced with $${exp}^{j\omega}$$ and I am aware of the identities $${... 1answer 39 views ### Z transforms doubt -(ROC and its purpose)! i had this doubt previously queried in another forum, but unfortunately had no answer. Consider a signal 3^n u[n]. Take its Z transform, which is Z/(Z-3). Now i know that in real sense, Z is a delay ... 1answer 34 views ### Determine transfer function based on a diagram with ai coefficients given From a diagram with input x(n) a summer and three feedback delay taps I get the difference equation...$$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:... 0answers 23 views ### 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]. 1answer 61 views ### 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 ... 1answer 62 views ### 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 ... 1answer 110 views ### 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 ... 1answer 33 views ### how to calculate H_{lp} = z(1- H_{hp})  , given coefficients for H_{hp}? 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-...
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 ...