# Questions tagged [self-study]

This tag means the asker is new to the DSP field and is requesting extra guidance. It has similar connotations to the homework tag, but this lets potential answerers know they should probably do more than guide the self-studier compared with the homework requester.

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### Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
1 vote
143 views

### How can I apply a filter to remove reverberation with python?

I am developing an algorithm that automates the processing of audio files for the assembly of datasets of machine learning models. Among the steps to be followed for the processing of the files is to ...
• 13
1 vote
21 views

### implement gradient descent with sparsification algorithm

I am trying to implement the algorithm in this paper for finding a sparse vector x that minimizes the square error $\lVert y − \Phi x\rVert_2^2$ where $\Phi$ need to satisfy the restricted isometry ...
• 155
56 views

### Magnitude spectrum of LTI system output signal

First year student so please excuse my lack of knowledge. As i understand i need to use convolution which is: $$y^{out}(t) = u^{in}(t) * h(t)$$ Or maybe my thoughts are wrong so please correct me. ...
1 vote
54 views

### Plotting the amplitude and angle spectre of this signal

I am looking clarification that I have the appropriate solution to this question, thoughts and tips to improve my understanding are also welcome! f(n) is a discrete sample of the following signal. ...
• 17
61 views

### Determining the full DFT values of X(k) given a partial sample [closed]

I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial. I am thinking that I am going to work back, I read the matlab documentation ...
• 17
81 views

### Expected value and autocorrelation

I have a wide sense stationary stochastic process ${{X_t;t\in \Re}}$ with mean 0 and autocorrelation function $R_x(\tau)=1-\frac{1}{4}|\tau|$ for $|\tau|=0,1,2,3;$ and zero anywhere else. I'm supposed ...
116 views

• 105
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### What does $\mathcal{ E}(|h|^2)$, where $|h|^2$ is power of the channel gain $h$ represent?

I came across this notation of $\mathcal{E}(|h|^2)$ in a research article. $h$ is the channel gain of a wireless communication channel. In particular, a Rayleigh fading channel. I know that $|h|^2$ ...
• 105
33 views

25 views

### Best way to compare audible alarms

I'm working on an alarm recognition program in MATLAB in which multiple reference audio samples of different alarms would be recorded. Afterwards, the program would sample every so often and compare ...
371 views

### Simulate butterworth filter with initial condition of state vector in R

I'm working in R with the packages signal and control (don't know wether these are even the best for my use case). I have a high ...
• 109
605 views

### Inverse system of sinc?

I'm doing some self-study for an important exam I'll have in late March and came across the following question: So, using the convolution properties, if I want to find an identity system so that the ...
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1 vote
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### Degradation of BPSK system using matched filter with a timing error

Given a BPSK system with: \begin{align*} s_1(t) &= Au_T(t) \\ s_2(t) &= -Au_T(t) \\ \end{align*} where $u_T(t)=1$ for $0<t<T$, and zero otherwise. Given $A > 0$, and Gaussian white ...
• 13
64 views

### Clarification on eigenfunction property from Oppenheim's Discrete-time signal processing, 3rd ed

Could anybody explain what is meant by the following statement on page 50 of Oppenheim and Schafer's book Discrete-Time Signal Processing (third edition)? The eigenfunction property of complex ...
527 views

### Power of an angle-modulated wave

Let $$\phi(t) = A\cos(\omega_c t + km(t)) \tag{1}$$ be an angle-modulated wave(FM or PM). What's the power of $\phi(t)$? Intuitively, it seems that the answer is $$P = \frac{A^2}{2} \tag{2}$$ since ...
• 726
459 views

### How can I find expansion coefficients of the a vector in a given basis?

How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors? Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$ What are the expansion ...
1 vote
167 views

### How to choose a fixed adaptation step for decision feedback equalizer

How do I choose $\mu$ - a value of a step size for adaptation in a decision feedback equalizer (DFE) with adaptive reference control (ARC)? For a regular adaptive FIR filter an adaptation step depends ...
• 396
88 views

### Even and odd components of a constant function [closed]

Let $x(t)= 1$ for all values of $t$. The even and odd components of $x(t)$ are ____ , _____ respectively.
288 views

### Discrete Time Convolution Evaluation

I'm trying to solve a problem on convolution from Alan V.Oppenheim: Find the convolution output $y[n]$ for the following signals: $$x[n]= u[n]\quad\text{and}\quad h[n]=a^{n}u[-n-1], \ a>1$$ I ...
• 211
1 vote
98 views

### Discrete-time Convolution Convergence Issue

I'm trying to solve a problem on convolution from Alan V.Oppenheim: Find the convolution output $y[n]$ for the following signals: $$x[n]= u[n]\quad\text{and}\quad h[n]=a^{-n}u[-n-1], \ a>1$$ I ...
• 211
1 vote
### Optimal receiver for a binary system employing waveform $s=A\cos^{2}(\pi f_c t \pm \alpha)$
I want to design an optimal (minimizing error probability) receiver for system of two waveforms (with $0<\alpha<\frac{\pi}{2}$): \begin{align} s_1 &=A\cos^{2}(\pi f_c t + \alpha)\\ s_2 &=...