# Questions tagged [math]

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### Fourier transform why can I convert one of the axes into an imaginary number?

Contextualizing This question is inspired by the following video: https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown I own a sign, a drawing of a square with 200 points ...
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1 vote
456 views

### Why Hilbert Transform is terrible choice for amplitude demodulation of broadband signals?

A reference answer empirically demonstrates that Hilbert envelope does not work well for the (amplitude) demodulation of a broadband signal. I am looking for the math which explains why...
37 views

### 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 ...
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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### 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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### 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 ...
1 vote
51 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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### 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,...
82 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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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
190 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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### 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 ...
• 101
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### 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
130 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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### 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. ...
• 103
247 views

### Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina , 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, $t$ - ...
1 vote
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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175 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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### 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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### 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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### 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
236 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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### 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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### 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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### 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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### 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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### 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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### 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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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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108 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 ...
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 $A(f)$, $B(f)$,...