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Questions tagged [math]

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Get IMU acceleration of a direction when tilted

I have an IMU that is placed on the body. My goal is to calculate the position data of the vertical upward movement. Since the sensor is never perfectly aligned and will always have a little tilt, I ...
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0 answers
25 views

Confusion Understanding the mathematical expression of duality property of dft?

Duality Property for DFT Above dsp.se question provides good understanding about dft duality property but i am having difficulty understanding its mathematical expression because on Google when i try ...
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5 votes
2 answers
100 views

What *is* pitch-shift?

As I understand it, pitch-shifting (without changing speed) and time-scaling (without changing pitch) are two sides of the same coin, because if we can do one we can get the other through resampling ...
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0 answers
60 views

How to Get Started On Demodulating Signals Such As Amplitude Modulation and Pulse Width Modulation

I'm looking to understand how signal modulation/demodulation works. My goal is to be able to demodulate a 315 MHz key fob and be able to tell what buttons are being pressed so I can have a Python ...
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1 vote
0 answers
29 views

How to find the kernel of the convolution?

I'm trying to solve the following exercise: Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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-1 votes
1 answer
85 views

I'm having problems simplifying this discrete-time fourier tranform

I have this problem, and I can't get to the solution. $$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty} {(0.6)^{|n|}[u(n + 10) − u(n − 11)]}e^{-j\omega n}$$ The solution is $$X(e^{j\omega}) = \frac{0.64 − ...
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0 votes
1 answer
64 views

How do I carry out SRT Radix-4 fixed-point division with more than a few bits?

I've managed to get a hand on how SRT division works, but I haven't been able to construct a working example. My current sticking point is that e.g. the Pentium floating-point division bug came about ...
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-2 votes
1 answer
27 views

what are the application of fourier transform in finding frequency response? [duplicate]

i need the application of Fourier transform in finding frequency response in mathematical terms
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3 votes
1 answer
85 views

Is it possible to compute the PSD of s(t)^2 given the PSD of s(t)?

Given a well-behaved signal $s(t)$ given by, $s(t) = \sum_{i}^{N} \cos( \omega_it + \phi_i) $ with a large $N$ and a well-known power spectral density (PSD), $\tilde{S_1}(\omega)$. Is it possible to ...
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0 votes
1 answer
121 views

False positive rate with CRC

What is the technique to calculate the false positive rate for an N-bit CRC? Example: Communication system sends M-bit packets with a N-bit CRC (M >> N) appended to each packet. What is the ...
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0 answers
58 views

Problem with the output self implemented “ Iterative FFT DIT Radix2 ” algorithm matlab

I´m trying to implement my own FFT with the iterative Radix2 algorithm (I even thought about using the recursive one but it seems Simulink doesn´t allow me to). I tried all of the possible variations ...
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1 vote
2 answers
71 views

Parseval's Theorem for Time Domain Data with DC

I have read several times that the variance for time domain data with a zero mean is equal to the integral of the power spectral density divided by N. From wikipedia, the discrete form of Parseval's ...
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1 answer
45 views

Different mathematical signal models for different applications

I am looking for some interesting and physically meaningful applications of different signal models. I am currently working with complex analytic signal model given below, but I couldn't come up with ...
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1 vote
0 answers
19 views

Backpropagation in a Network [closed]

Hi does anyone know how to solve this. Im really struggling to figuring this one out. I am unclear of how the backpropagation part would work in this network and how to calculate it for each weight. ...
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1 vote
1 answer
85 views

Calculating Haar features

I am confused on how to solve this problem, does anyone have any ideas? https://www.merl.com/publications/docs/TR2004-043.pdf For a Haar filter $H \in \mathbb{R}^{3 \times 5}$ defined as below: What ...
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2 votes
1 answer
209 views

Digital integrator

I have been implementing a control software where I need to calculate a magnetic flux based on the measurement of the phase voltages of a three phase grid (basically three sinewaves) according to the ...
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  • 231
1 vote
2 answers
117 views

Question about delayed sampled sinusoid math expression

I have been studying the digital audio processing by using the book <Designing Audio Effect Plugins in C++>. For analog Sinusoid: Complex Sinusoid = $e^{jωt}$ Delayed Sinusoid = $e^{jω(t−n)} = e^...
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7 votes
1 answer
119 views

Why Does the Median Filter Minimize the Absolute Value Error $L_1$ Cost Function?

I can easily prove that the mean filter minimizes the square error $L_2$ cost function using simple calculus. However, how do you prove that the median filter is optimal with respect the absolute ...
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0 votes
1 answer
46 views

mathematical expression to detect modulated data within a vector

Assume I have such modulated data which is, for example, $x=0.7+0.7i$. That modulated data is encapsulated in a vector as below: OR where $c$ is any constant number, let’s say, for example: $c=0.7$ ...
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1 vote
1 answer
48 views

Effectively extracting “real” data from a noisy dataset

This question was originally posed to Math SE. It was suggested that DSP SE would be more suitable. Background & Motivation: I have three lists of timestamps (UNIX timestamps, plus a subsecond ...
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0 answers
21 views

Is it important to learn to find de period of the sum fo two DT signals?

The fundamental period (N) of the sum of two DT signals could be the LCM of the fundamental periods. However, this is not always the case. I would like to know wether, during engineering design or ...
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0 answers
32 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
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1 vote
2 answers
388 views

Problems computing the DFT of finite length sequence

I am having trouble finding the same answer as the solution manual for this sequence. The problem asks to compute the DFT of $$ x[n] = \begin{cases} 1 & \text{for even } n \in \{0\...
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  • 113
1 vote
1 answer
157 views

Linear correlation of two vectors?

We had a lecture on digital watermark detection using linear correlation. Here it was explained that the linear correlation of two vectors is equal to their scalar product divided by the dimension. So,...
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0 votes
1 answer
75 views

Relation between the matrix trace and the amplitude of each element

Assume a diagonal matrix $\mathbf X$ whose size $N\times N$ and its diagonal elements are $0.5 + 0.5i$, and the vector $\mathbf p$ of size $N\times 1$ whose elements have similar amplitude. I have ...
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2 votes
2 answers
1k views

DFT of pure sinusoidal wave

I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to ...
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1 vote
1 answer
158 views

SNR for the magnitude of a complex signal

The SNR for a complex valued signal is presented by Dilip Sarwate in: https://dsp.stackexchange.com/a/42359 Following the same steps I would like to estimate the SNR for the magnitude of a complex ...
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0 votes
1 answer
35 views

I don't understand how the zeros are found of this 2nd order feed-forward filter

I realized someone asked a question about the exact same section of a book, which can be found here: Question about zeroes of simple 2nd order FIR filter. While the answer to this question looks ...
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2 votes
2 answers
850 views

Coordinate system in digital image processing

I am trying to understand image coordinate system where I read that it is reversed. So if $f(x,y)$ is actually $f(y,x)$ where $f(\cdot, \cdot)$ is the image. I am a bit confused and would appreciate ...
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1 vote
1 answer
113 views

Summations in Z-Transform

I'm currently working on a problem that involves a Z-Transform. Basically, the essence of the problem is that if: \begin{equation} H\left(z\right) = \sum_{n=0}^{N-1}h\left(n\right)z^{-n} \end{equation}...
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0 votes
1 answer
49 views

Adding attenuations in dB

I am writing a synthesizer. One part of the synthesizer specification says that different sources can specify an attenuation to be applied to a signal, and that these attenuations should be summed. ...
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2 votes
0 answers
218 views

Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina [1], can be described by the following formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where, $t$ - ...
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1 vote
0 answers
76 views

Problem with natural logarithmic function in fixed point notation

I am facing a problem with natural logarithmic function in fixed-point notation. Let's say $$x = 0.54, \qquad\text{then}\qquad \ln(x) = -0.616186, \qquad\text{a negative number} \tag{1}$$ Then in ...
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1 vote
1 answer
150 views

FFT algorithm gives wrong signs on my output numbers

I was told from another stack exchange (stackoverflow and computer science stack exchange) to post here - so hopefully now i can get some help from people who understand the algorithm, but if this is ...
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5 votes
1 answer
146 views

Why Cramér spectral representation and not DTFT for stochastic process

In a lot of time-series analysis references I find (written by mathematicians or statisticians rather than engineers), I find the following signal decomposition for a stochastic process, termed the &...
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14 votes
6 answers
30k views

What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
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0 votes
1 answer
50 views

Solve equations with conjugates multiplications

If I have a two variables $x_1$, $x_2$ and two equations. In the first equation the first variable $x_1$ is multiplied with the conjugate of same number which is multiplied with $x_2$, and in the ...
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1 vote
1 answer
220 views

Finding the system output by convolution

pretty new to this concept, so do bear with me. A linear dynamic system is described by the following differential equation: Transfer function H(s) is calculated to be = I've already found the ...
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0 votes
4 answers
74 views

On the simplification using trigonometric functions

Assume I have a matrix $D$ whose its entries are as below : Where $A$ and $B$ can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? ...
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0 votes
1 answer
176 views

Calculate autocorrelation of a sinus

I am a beginer in signal processing. I am currently studying a signal $s(t) = \cos(h(t))$, and I have to calculate its autocorellation. Since $h(t)$ is periodic of period $T_s$, I calculated the value ...
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0 votes
2 answers
295 views

Q format doubts

Is my understanding correct w.r.t Q format. signed Q15.1 format means, 15 bits for fractional and 1 for integer bits SO max range is - 2^15 / 2^15 to + (2 ^ 15 - 1) / 2^15 signed Q7.0 means, 7 bits ...
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1 vote
2 answers
54 views

Understanding Communication Theory Jargon for Statistical Linear Models

Coming from a statistical background, I understand the following formula: \begin{equation} y = X\beta + \epsilon \end{equation} as a linear regression model, with data input-output pair: $(X,y)$, ...
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1 vote
3 answers
9k views

Convolution of two rectangular pulses intuition

From what I understand the convolution of the impulse response of a system with the input to that system gives the output. Now if the impulse response is a rectangular function and the input is also ...
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2 votes
1 answer
282 views

Absolute value based AM envelope detection viewed in the frequency domain

In my understanding when a passband AM signal is demodulated with an envelope detector taking the absolute value restores the original baseband version of the signal and the low-pass filter removes ...
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  • 237
1 vote
1 answer
193 views

Separation of signals without loss of information about the signals themselves

There is a signal that contains: Rectangular pulses on frequency of 1 kHz Rectangular pulses on frequency of 1.4 kHz Other noises. Required: Separate 1kHz pulses from everything else and measure ...
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1 vote
1 answer
105 views

Dummy DSP student request for IDTFT Calculation and Integration Process

We have one DSP course in biomedical engineering, so i have been for 10 years away from mathematical calculation and working in this years by programing by c and ..., so one of our exercise is to ...
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0 votes
0 answers
46 views

Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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2 votes
0 answers
617 views

Derivation of ZOH Discretization

I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps. I think I understand the first part, this is just the ...
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  • 191
1 vote
3 answers
2k views

Resolution of Discrete Fourier Transform is 1/T - Mathematical proof?

In many articles I see that the frequency resolution of the Discrete Fourier Transform (DFT) equals Fs/N where Fs is the sampling rate and N is the total number of samples. Fs/N is equivalent to 1/T ...
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1 vote
0 answers
315 views

Power, energy and amplitude spectrum from fft in MATLAB - scaling

I've looked at previous answers and none of the answers seem to agree (perhaps I'm missing something obvious): I would like to know what the correct scaling to use is for amplitude, energy and power ...
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