# Questions tagged [homework]

Homework means the asker is requesting help with school homework. This lets potential answerers know that they should guide the student in solving the problem, rather than simply showing the complete answer.

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### Find Discrete Fourier transform given the inverse

I don't know if this question is already answered somewhere else but I'm stuck with that and I need help... Given an inverse Discrete Fourier Transform (IDFT), with N=16 : How can I find the F(k) ...
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### Finding the Period of a Signal by Its DTFT Data

find period of DTFTs where vertical lines represent Dirac deltas
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### Distinguishing FIR and IIR from difference equation

Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$ I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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1 vote
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### Clarification on Discrete-time convolution and signal shifting

What are $y_1[n]=x_1[n]*h[n]$ and $y_2[n]=x_2[n]*h[n]$? $$x_1[n]=(0.1)^nu[n],\quad x_2[n]=(0.2)^n,\quad h[n]=(0.3)^nu[n]$$ I am confused about how to calculate $y_{1}[n]$. The formula for discrete ...
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### How to sketch the following discrete time signal $\sum_{k=0}^{n} \delta[n-k]$?

I tried to solve it like in the picture but It feels so wrong though.
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### Fourier Coefficients

Consider the signal $$x(t)=\cos(2\pi t)$$ Since $x(t)$ is periodic with a fundamental period of $1$, it is also periodic with a period of $N$, where $N$ is any positive integer. What are the ...
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### Step response given impulse response $h = e^{-|t|}$

I was given the above homework problem and I know how the step response is achieved, but I'm not sure how to set up the integrals in order to evaluate the problem. I've attached my work, but it is ...
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If $h(n)$ is the impulse response of the discrete LTI system, $x(n)$ is the white noise process with variance $\sigma_x^2$ and $y(n)$ is the output, prove that $$\mu_y = \mu_x \, \sum_{k=0}^\... 0 votes 0 answers 368 views ### Equation for impulse train I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both 1 – so that f(x) has value 1 at x = 1,2,3,4... and f(x) has ... 1 vote 1 answer 312 views ### Time-variance and causality of y(t)=\sum_{k=-\infty}^{+\infty}x(t)\delta(t-kT) Is the following system time invariant and/or causal?$$y(t)=\sum_{k=-\infty}^{+\infty}x(t)\delta(t-kT)$$I think that it isn't time invariant and it is causal, and my thought is based on the ... -1 votes 1 answer 1k views ### How do I find the ROC of a system if it has no poles The output of a system of discrete time y[n] is corellated with the input x[n] through the equation y[n].$$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)It then asks me to find the system ... 0 votes 1 answer 591 views ### Time-invariance, causality and stability of h(t) of four given systems Question: The impulse response functions of four linear systems S_1,\ S_2,\ S_3,\ S_4 are given respectively by \begin{align} h_1(t)&=1\\ h_2(t)&=u(t)\\ h_3(t)&=\frac{u(t)}{(t+1)}... 2 votes 1 answer 482 views ### Find Fourier Transform of signal that satisfies this equation I have attempted it this way: G(j\omega) is a rectangular pulse in frequency domain. Using results, inverse Fourier transform of G(\omega) will beg(t)=\frac{\sin(2t)}{\pi t}$$Now given that ... 1 vote 1 answer 1k views ### How to find inverse of convolution integral? If x^{-1}(t) and  y^{-1}(t) denote the integrals of x(t) and y(t) defined by x^{-1}(t)=\displaystyle\int_{-\infty}^{t} x(\lambda)d\lambda y^{-1}(t)=\displaystyle\int_{-\infty}^{t}y(\lambda)d\... 2 votes 2 answers 9k views ### how to evaluate derivative of convolution integral? If the signal x(t) has ordinary first derivative \dot x(t), then \dfrac{d}{dt}\big(x(t)\star y(t)\big) is: (a) \dot x(t)y(t) (b) x(t)\dot y(t) (c) \dot x(t)\star y(t) (d) \... 1 vote 1 answer 2k views ### Time shifting and time reversal For the problem given in the fig. how to solve it? My approach: Let y(n) be the first output (e.g for 1st case output of system A is y_1(n); for 2nd case output of system B is y_2(n), then ... 1 vote 1 answer 526 views ### Drawing the modulus from a Transfer function As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks In this exercise from an exam i was given that transfer function with poles and ... 0 votes 1 answer 38 views ### Evaluating different inputs into a given system We need to find which signal wont be the same after going through this sytem. My approach is this one: I took the filters frequency and did 2pi * 1/4 and gave me this "limit" 1.5707 (2pi because ... 2 votes 2 answers 298 views ### Finding the correct x[n] from a given DFT x[k] [closed] I'm struggling to solve this question from an exam. The question gives you a set of IDFTs from a given DFT, only one of those is the correct. The first thing I did is notice that 2\sin(\pi k) will ... 2 votes 1 answer 2k views ### proof of Autocorrelation property of DFT I am facing problem in proving the Auto-correlation property of Discrete Fourier Transform (DFT), that is$$\mathcal{DFT}\left\{\sum_{r=0}^{N-1}x[r]x^*[r+n]\right\} = X[k]X^*[k]= |X[k]|^2$$where X[... 0 votes 2 answers 1k views ### Inverse system of a system with integral I am trying to find the inverse system of the following (I tried finding the mathematical inverse function but since it is not the same I am not so sure) . Can someone help me find it?$$ y(t)=\int_{... 