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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1answer
109 views

difference equation block diagram delay or advance confusion

When does the unit delay, become unit advance essentially. Goal is to deduce difference equation from block diagram. Green text is notes about what the value should be in that node of the diagram. ...
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1answer
310 views

How to represent impulse function in 2D?

To be more specific I want to show that impulse function in 2D can be represented as $β(r)=δ(r)/πr$. Also I want to show that each projection of a two dimensional impulse function at the origin is a ...
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1answer
30 views

What reference power should I use?

My professor asked me to convert following powers into decibels: 15W, 25W, 33W, 450mW, 24MW, 44 GW,120pW. I know that decibels are about ratio power/reference_power. I don't have reference power ...
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1answer
44 views

DFT as an Orthogonal Basis Change

In one of the homeworks that I am dealing with for Linear Systems course, I have encountered with such a statement: Consider $\mathbb{C}^N$ the vector space of N dimensional complex vectors. We can ...
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1answer
81 views

Steady state value of a complex convolution

I am trying few problems on the introductory part of DSP. One of the problem asks to calculate the steady state response of a system with impulse response $h[n] = (\frac{j}{2})^{n} u[n] $ to an input ...
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1answer
100 views

classify the system if it's linear , non-linear , time variants or invariants [closed]

classify the system if it's linear , non-linear , time variants or invariants
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1answer
57 views

Finding the transfer function of a discrete signal described by two equations

A discrete time system is described by the following system of equations. $$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$ $$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$ Find the systen function and then find the ...
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1answer
163 views

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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1answer
195 views

Convolution of Input signal and Impulse response

I can solve the output if the input is $$ x[n] = \delta[n+1] + \delta[n] + 2\delta[n-1] + \delta[n-2]$$ and the impulse response is $$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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2answers
819 views

FFT vs DFT Run Time Comparison (Complexity Analysis) in MATLAB

So we were given an assignment to plot the time taken by the FFT algorithm by MATLAB and a DFT algorithm written by me in MATLAB.G The expected output should have been the DFT algorithm following the ...
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1answer
2k views

Maximum Likelihood Detection of Signal Vectors in Gaussian Noise

Consider a binary-input additive white Gaussian noise channel. Let $\mathbf{x}_0 = (\sqrt{Es},\sqrt{E_s},⋯,\sqrt{E_s})$ and $\mathbf{x}_1 = (-\sqrt{E_s},-\sqrt{E_s},⋯,-\sqrt{E_s})$, be two codewords ...
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1answer
33 views

How to make sinewives with array input, for-loop functions and operate array with others [matlab]? [closed]

Thanks to previous question, I got some clues to resolve this one. But, I still get some problems here. ...
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1answer
90 views

Band pass filter (digital resonance)

Q1:  Consider a discrete-time band-pass filter (BPF) that uses only two poles as $$ H(z) = G \frac{1}{\big(1-r \, e^{j \omega_0} z^{-1}\big)\big(1-r \, e^{-j \omega_0} z^{-1}\big)} $$ where this ...
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1answer
370 views

Calculate the Output of Linear Time Invariant System Given it Impulse Response [closed]

A filter is defined as $ h \left[ n \right] = \delta \left[ n \right] - \delta \left[ n - 1 \right] $. Given a signal $ h \left[ n \right] $ defined as: $$ x \left [ n \right ] = \begin{cases} 1 &...
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0answers
254 views

Finding the Period of a Signal by Its DTFT Data

find period of DTFTs where vertical lines represent Dirac deltas
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1answer
68 views

Properties of DTFT to Infer the Inverse DTFT of Altered Data [closed]

Given a signal $ x \left[ n \right] $ and its DTFT $ X \left( {e}^{j \omega} \right) $. Which property of the DTFT allows you to easily compute the inverse DTFT of $ \frac{4 X \left( {e}^{j \omega} \...
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1answer
882 views

Calculate the Inverse DTFT of the DTFT Derivative in Terms of $ x \left[ n \right] $

Consider the signal $ x \left[ n \right] $ and its DTFT transform $ X \left( {e}^{j \omega} \right) $. Assume $ X \left( {e}^{j \omega} \right) $ is differentiable. What is the Inverse DTFT of: $$ j ...
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1answer
171 views

How to evaluate CCDE at a given frequency?

Consider the following Constant Coefficient Difference Equation (CCDE) given below $$y[n] - \frac{1}{2}y[n-1] = 2x[n] - 5x[n-1] - x[n-2]$$ Let $H(e^{j\omega})$ denote the transfer function of this ...
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1answer
53 views

Meaning of a formula about transient frequency bins

I'm trying to understand the following formula in this paper: Sadly, the paper does not define most of the symbols it is using, so my guesses so far are: $T_{tr}$ refers to the sampling interval i....
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1answer
35 views

Signal analysis using a buffer [closed]

I am performing an analysis of an output signal in the interval $t<0$ from the operational amplifier given in the following image where $v_{C_1}(0^-)$ and $v_{C_2}(0^-)$ are the initial conditions ...
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1answer
2k views

Determine if $ y[n] = ny[n-1] + x[n]$ is linear time invariant and BIBO stable

Check if the following system is linear time invariant and BIBO stable.. $$ y[n] = ny[n-1] + x[n] $$ for $n\ge 0$. We are also given that the system is at rest (i.e. $y[−1] = 0$). I know that to ...
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1answer
986 views

Ratio of the power in the sidebands to the total power in conventional AM

Message signal and carrier signal are given as $m=\cos(2 \pi \cdot f_{m} \cdot t) $ $c=A_{c}\cdot \cos(2 \pi \cdot f_{c} \cdot t) $ I was asked to find modulation index $a$ so that ratio of the ...
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1answer
42 views

Need help deriving the energy of a signal

I am solving old exam problems in preparation of my exam in signals, and I'm having trouble with a question. For a continuous aperiodic signal with the spectrum $X(\omega)=\exp(-\omega^2)$ I am to ...
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1answer
71 views

Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?

I have been staring at this problem for a week now... Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
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1answer
294 views

Pole zero plot, normalizing frequency response plot?

I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram. $$ H(z) = H_0 \frac{\prod\limits_{m=1}^{M} (z - q_m)}{\prod\limits_{m=1}^{M} (z - p_m)}$$ $$ H(e^{i\omega}) =...
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1answer
94 views

Is this two input discrete system linear? [closed]

Given two inputs $\: x_1[n]\: x_2[n]\:$Is the system $\:y[n]=x_1[n]\times x_2[n]\:$ linear ? My Approach: $(x_1\times x_2)[n]=S_1[n]\rightarrow Y_1[n]$ $(x_3\times x_4)[n]=S_2[n]\rightarrow Y_2[n]$ $...
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3answers
829 views

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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1answer
9k views

How to find the phase spectrum of a rectangular pulse? (Fourier Transform)

How to find the phase spectrum of a rectangular pulse? The Fourier transform of a rectangular pulse $$ x(t) = \begin{cases} 1, & \text{for $|t| \le \tau /2$ } \\ 0, & \text{otherwise} \end{...
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2answers
341 views

Interpolation and decimation

I have a sinusoid in continuous time, with a frequency of 18kHz, it is sampled ideally with a continuous to discrete convertor, with a frequency of 27kHz. After that, we change the sampling speed in ...
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1answer
49 views

impulse response of a system from its step response;confusion

If the step response of a system is given as $$c(t)=(10e^{-5t}-2e^{-10t}+1)u(t)$$ then its impulse response is _______? My Approach: we know: $$h(t)= \frac {d}{dt} c(t)$$ Process(1): $$h(t)= \{ ...
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1answer
53 views

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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1answer
380 views

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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1answer
89 views

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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1answer
410 views

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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1answer
84 views

Fourier components of $\cos(2\pi f_1t)$

I have the signal $s(t) = \cos(2\pi f_1t)$ and I am looking for its components vs the Fourier basis, over the interval $[0, T]$. The formula for computing the coefficients is $$ s_n = \int_{t_0}^{t_1} ...
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1answer
44 views

Pulse wave question

Wikipedia, fount of all knowledge (Ha! LOL), gives a formula for a pulse wave here: The formula is: $$f(t)=\frac{\tau}{T}+\sum_{n=1}^{\infty}\frac{2}{n\pi}\sin\left(\frac{\pi n \tau}{T}\right)\cos\...
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1answer
56 views

Proof of $E[y(n)]=E[x(n)] \, \sum h(k)$

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}^\...
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0answers
176 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 ...
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1answer
86 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 ...
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1answer
253 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 ...
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1answer
129 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)}...
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1answer
135 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 be $$g(t)=\frac{\sin(2t)}{\pi t}$$ Now given that $...
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1answer
635 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\...
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2answers
3k 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) $\...
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1answer
800 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 ...
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1answer
190 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 ...
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1answer
32 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
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2answers
106 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 ...
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1answer
1k 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
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2answers
477 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_{...