# 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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### Impulse response of a causal system from transfer function in z-domain

The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$ I need to find the impulse response h[n] of a causal system with x[n] as unit impulse. I have tried to find the impulse response by the following ...
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### Explicit a succession using z inverse transform

Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?: $y(0) = 1 \\ y(n+1) = 2y(n) + 3$ I can't write ...
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### Finding Z transform of a signal: Intermediate steps

Find the Z transform of $y(n)=x(n+2)u(n)$ I have solved the problem. I have doubt whether it is correct or not. It would be very helpful if someone could check whether the steps that I have ...
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### Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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### $\mathcal Z$-Transformation in Discrete Time [closed]

I want to find the inverse $\mathcal Z$-transform of this, in discrete time: $$X(z) = \frac{1}{1+3z^{-1}+2z^{-2}}$$
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### LTI system phase response given $z$-transform

I have been given this question \begin{equation} H\left(z\right)\:=\:\frac{1}{6}\left(1+z^{-2}\right)^6 \end{equation} (a) Compute and plot the phase response of the system. (b) Determine ...
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### How to compute the Laplace transform of a discrete signal?

Assume I have a discrete random signal, $f(t)$ for which I want to calculate the laplace transform. How can I do it in matlab without using sym variables, for ...
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### ROC of transfer function

given: $$H(z) = \frac{4z(z-1)}{z-0.5}$$ I would say, when all poles are in the unit circles, the impulse response is right sided and causal.
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### How does a digital filter $H(z)=1/(1-z^{-1})$ change a continuous rectangular pulse? [closed]

I inputted the following signal in this discrete time filter and got this output Could anyone explain how ? Also how does a discrete filter process a continuous time output ?
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### why is the z transform transfer function 1/(z-1) called an integrator?

I am reading up on delta sigma modulators and there this term $\frac{1}{z-1}$ that appears repeatedly and is referred to as an "integrator". Why is this so ?
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I'm looking at an example on how to obtain the $\mathcal Z$-transform from a finite length truncated exponential sequence, namely: $$x[n] = \begin{cases} a^N &\text{for} & 0 \leq n \leq N-1\\... 2answers 2k views ### Conjugate reciprocal pairs of zeros and poles in FIR design Assuming the impulse response h[n] of an FIR filter is real for all n, Why are zeros and poles in FIR design found in reciprocal and conjugate pairs? Is the assumption necessary for this ... 1answer 100 views ### What do I with the sampling period when I inverse \mathcal Z-transform? Given the input$$e(kT_s) = {0.4, 0.8,1.2, - 0.9}, \quad k = 0,1,2,3$$and transfer function$$T\left(z^{-1}\right)=\frac {z^{-1}-0.8z^{-2}}{1-1.1z^{-1}+0.3}$$Find the output Y(kT_s),\... 2answers 409 views ### Design discrete controller for zero steady state error I have the following system where$$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ... 1answer 104 views ### Find transfer function given impulse I am given the following discrete time transfer function :$$G_d(z^{-1})=z^{-d}\frac{b_0+b_1z^{-1}}{1+a_1z^{-1}}$$which has the following impulse response$$g_d[n]=\{0,1,-0.1,-0.05,...\}$$How can I ... 1answer 1k views ### How to find out the transfer function of a FIR filter?$$h[n]=\begin{cases}a^n & \text{if } 0 \le n < N \\ 0 & \text{otherwise}\end{cases}$$And for which values of a the filter is stable I know that the transfer function will be$$H(z)=\...
Let's suppose I have to find the impulse response of a discrete time LTI system given a specified input and its output through the system. I think I'm going to get the $\mathcal Z$-transform of input-...