# Questions tagged [math]

The tag has no usage guidance.

158 questions
Filter by
Sorted by
Tagged with
1 vote
47 views

### What is the effect of multiplication on the value of discontinuities?

I see that the values of a distribution at discontinuities are essentialy equal to the mean of the right-hand and left-hand limit values when dealing with distributions in relation to the Fourier ...
66 views

### How to handle undefined functions in a convolution?

When convolving with undefined functions, do we just treat them like variables? (eg. How do I handle $u \left( k \right)$ and $u \left( n - k \right)$ since they are just step functions with no ...
13 views

### How to handle imaginary numbers with total square error questions

I am pretty new to algrebra so if u can use simple terms and explain a bit more it would be helpfull. Ive been trying to use imaginary numbers to get the total square error of a graph of a non linear ...
58 views

### Improving Modeling of Thermal Noise Behavior at Antenna

Background I recently asked this question over on Electrical Engineering Stack Exchange. On the advice of some commenters there, I've broken off those pieces which are appropriate for asking as ...
27 views

### Improving Modeling of Thermal Noise Propagation Through a Signal Chain

Background I recently asked this question over on Electrical Engineering Stack Exchange. On the advice of some commenters there, I've broken off those pieces which are appropriate for asking as ...
163 views

204 views

### Ambiguity function volume

I find myself confused how two properties of the ambiguity function relate to one another. The properties in question are (presented here from wikipedia, but similar formulas can be found in books by ...
2k views

### Under what conditions does DFT(f(x)) = f(DFT(x)) hold?

I have encountered a text (a specification) in which $$\text{FFT}\left(f\left(x\right)\right) = f\left(\text{FFT}\left(x\right)\right)$$ is clearly presumed (for the functions they are applying). Thus,...
855 views

### Time shifting a signal in python

I am currently modeling FMCW (linear FM) and SFCW (stepped FM) chirps in python. For my project, I need to simulate those signals as a transmit chirp and a received one, scattered from point targets ...
245 views

### Pole Quantization Patterns in 2nd Order IIR Resonators

Background My typical approach to fixed point design for digital filters is to iteratively scale and increase quantization while comparing the fixed point simulation to the floating point design ...
42 views

### 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 ...
2k 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...
319 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 ...
49 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 ...
382 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 ...
1 vote
813 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 ...
186 views

### How to Find the Kernel of the Convolution for Linear Interpolation?

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 ...
92 views

1 vote
376 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,...
133 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 ...
3k 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 ...
347 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 ...
42 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 ...
2k 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 ...
1 vote
230 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}...
238 views

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. ...
338 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
79 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 ...
1 vote
293 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 ...