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.
390
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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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2
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1
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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
$$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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FFT vs DFT Run Time Comparison (Complexity Analysis) in MATLAB
So we were given an assignment to plot the time taken by the FFT algorithm by MATLAB and a DFT algorithm written by me in MATLAB.G
The expected output should have been the DFT algorithm following the ...
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Maximum Likelihood Detection of Signal Vectors in Gaussian Noise
Consider a binary-input additive white Gaussian noise channel.
Let $\mathbf{x}_0 = (\sqrt{Es},\sqrt{E_s},⋯,\sqrt{E_s})$ and $\mathbf{x}_1 = (-\sqrt{E_s},-\sqrt{E_s},⋯,-\sqrt{E_s})$, be two codewords ...
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How to make sinewives with array input, for-loop functions and operate array with others [matlab]? [closed]
Thanks to previous question, I got some clues to resolve this one.
But, I still get some problems here.
...
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1
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203
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Band pass filter (digital resonance)
Q1: Consider a discrete-time band-pass filter (BPF) that uses only two poles as
$$ 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)} $$
where this ...
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1
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Calculate the Output of Linear Time Invariant System Given it Impulse Response [closed]
A filter is defined as $ h \left[ n \right] = \delta \left[ n \right] - \delta \left[ n - 1 \right] $.
Given a signal $ h \left[ n \right] $ defined as:
$$ x \left [ n \right ] = \begin{cases}
1 &...
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558
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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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1
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725
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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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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:
$$ j ...
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594
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How to evaluate CCDE at a given frequency?
Consider the following Constant Coefficient Difference Equation (CCDE) given below
$$y[n] - \frac{1}{2}y[n-1] = 2x[n] - 5x[n-1] - x[n-2]$$
Let $H(e^{j\omega})$ denote the transfer function of this ...
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Meaning of a formula about transient frequency bins
I'm trying to understand the following formula in this paper:
Sadly, the paper does not define most of the symbols it is using, so my guesses so far are:
$T_{tr}$ refers to the sampling interval
i....
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Signal analysis using a buffer [closed]
I am performing an analysis of an output signal in the interval $t<0$ from the operational amplifier given in the following image
where $v_{C_1}(0^-)$ and $v_{C_2}(0^-)$ are the initial conditions ...
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Determine if $ y[n] = ny[n-1] + x[n]$ is linear time invariant and BIBO stable
Check if the following system is linear time invariant and BIBO stable..
$$
y[n] = ny[n-1] + x[n]
$$
for $n\ge 0$. We are also given that the system is at rest (i.e. $y[−1] = 0$).
I know that to ...
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Ratio of the power in the sidebands to the total power in conventional AM
Message signal and carrier signal are given as
$m=\cos(2 \pi \cdot f_{m} \cdot t) $
$c=A_{c}\cdot \cos(2 \pi \cdot f_{c} \cdot t) $
I was asked to find modulation index $a$ so that ratio of the ...
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Need help deriving the energy of a signal
I am solving old exam problems in preparation of my exam in signals, and I'm having trouble with a question.
For a continuous aperiodic signal with the spectrum $X(\omega)=\exp(-\omega^2)$
I am to ...
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Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?
I have been staring at this problem for a week now...
Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
user35668
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Pole zero plot, normalizing frequency response plot?
I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram.
$$ 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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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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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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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
$$ x(t) =
\begin{cases}
1, & \text{for $|t| \le \tau /2$ } \\
0, & \text{otherwise}
\end{...
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2
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650
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Interpolation and decimation
I have a sinusoid in continuous time, with a frequency of 18kHz, it is sampled ideally with a continuous to discrete convertor, with a frequency of 27kHz. After that, we change the sampling speed in ...
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impulse response of a system from its step response;confusion
If the step response of a system is given as $$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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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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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
$$
s_n = \int_{t_0}^{t_1} ...
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Pulse wave question
Wikipedia, fount of all knowledge (Ha! LOL), gives a formula for a pulse wave here:
The formula is:
$$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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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
$$\mu_y = \mu_x \, \sum_{k=0}^\...
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Equation for impulse train
I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both $1$ – so that $f(x)$ has value $1$ at $x = 1,2,3,4...$ and $f(x)$ has ...
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Time-variance and causality of $y(t)=\sum_{k=-\infty}^{+\infty}x(t)\delta(t-kT)$
Is the following system time invariant and/or causal?
$$y(t)=\sum_{k=-\infty}^{+\infty}x(t)\delta(t-kT)$$
I think that it isn't time invariant and it is causal, and my thought is based on the ...
user33199
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How do I find the ROC of a system if it has no poles
The output of a system of discrete time $y[n]$ is corellated with the input $x[n]$ through the equation $y[n]$.
$$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)$$
It then asks me to find the system ...
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Time-invariance, causality and stability of $h(t)$ of four given systems
Question:
The impulse response functions of four linear systems $S_1,\ S_2,\ S_3,\ S_4$ are given respectively by
\begin{align}
h_1(t)&=1\\
h_2(t)&=u(t)\\
h_3(t)&=\frac{u(t)}{(t+1)}...
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Find Fourier Transform of signal that satisfies this equation
I have attempted it this way:
$G(j\omega)$ is a rectangular pulse in frequency domain. Using results, inverse Fourier transform of $G(\omega)$ will be $$g(t)=\frac{\sin(2t)}{\pi t}$$
Now given that $...
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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\...
user33321
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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) $\...
user33321
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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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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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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 ...
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2
answers
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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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1
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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$$
where $X[...
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Inverse system of a system with integral
I am trying to find the inverse system of the following (I tried finding the mathematical inverse function but since it is not the same I am not so sure) . Can someone help me find it?
$$ y(t)=\int_{...
user33117
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1
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Convolution including $\delta(t-5)$
I know the two properties of convolution that are related to my question
$\quad x(t)*\delta(t)=x(t) $
$\quad x(t)*\delta(t-t_0)=x(t-t_0)$
But my question is, how can I use those two to calculate $$ ...
user33117
1
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1
answer
586
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Cross-correlation - Why is there a complex part after FFT/IFFT when deleting the mirrored part of the spectrum?
I want to detect a special shape in my time series and I apply an matched filter using cross-correlation to increase the SNR.
...
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3
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199
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different moving average filters differences
Suppose we want to use a moving average filter (3-point moving average) for $X[n]$ (where $Y[n]$ is output). What are the differences among
$Y[n]=\frac13X[n-1]+\frac13X[n]+\frac13X[n+1]$,
$Y[n]=\...
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Impulse response function from pole-zero graph
I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula:
$$
W(s) = \frac{\rm ...
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2
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2k
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How to find $h[n]$ system response of this equation?
$2y[n-2]-2y[n-3]-4y[n-4]=x[n]-10x[n-1]-4x[n-2] + 4x[n-3]$ is the system that I'm looking for the response.
I transformed this system via using Z transform:
$$\frac{Y(z)}{X(z)}=H(z)=\frac{z^4 - 10z^...
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1
answer
615
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Find the coefficient of an AR-model
How can I infer the coefficients for an AR(2) model given an autocorrelation plot?
What I have tried so far: I can see this a cos-wave of 0.4 Hz, and then i find the values for each step $(1, 0.9211, ...
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422
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Autocorrelation and PSD
Let $X(t)$ and $Y(t)$ be two orthogonal processes with power spectral densities
$$S_{xx}(f) = S_{yy}(f)=\begin{cases}
1-\lvert f\rvert, & \lvert f\rvert<1
\\[1ex]
0,& \text{otherwise}
\end{...
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