# Questions tagged [time-frequency]

The tag has no usage guidance.

175 questions
Filter by
Sorted by
Tagged with
5k views

### What's the difference between the Gabor and Morlet wavelets?

The Gabor wavelet is a kind of the Gaussian modulated sinusoidal wave (source)   Gabor wavelets are formed from two components, a complex sinusoidal carrier and a Gaussian envelope. (source) ...
3k views

### Why LTI system cannot generate any new frequencies?

Why $Y (\omega) = X(\omega)H(\omega)$ implies that an LTI system cannot generate any new frequencies? Why if a system generates new frequencies, then it is not LTI?
925 views

### Least Squares Re Synthesis of Short Time Fourier Transform (STFT)

Working with my own MATLAB implementation of the short-time Fourier transform (STFT), I've managed to write code for the analysis step where a 1D time-domain signal $s[t]$ is progressively windowed, ...
2k views

### Match Filter in Time-Frequency domain instead of just Time domain. Redundant, or better?

Assume you have a signal, and within it, some pulses are present. A pulse is a simple tone. You know the pulses' duration and shape. (Let us assume that a pulse is made of a couple of cycles, and then ...
2k views

### Fourier Transform with both Time Delay and Frequency Shift

I know that the Fourier transform of a function with time delay can be written as: $$\mathscr{F}\big\{x(t-t_0)\big\}=X(f)e^{-j2\pi f t_0}$$ The Fourier transform of a function with frequency shift ...
2k views

433 views

### Mathematical model of equivalent-time sampling, the resulting unevenly spaced periodic signal, and its interpretation

I sample a continuous signal $s(T)$ over time. This leads to $s[t]$, which depends on several factors of which some are (pseudo-) periodic. I am interested in the effect of one such periodic factors ...
764 views

### what is continuous wavelet (cwt) ,wavelet packet (wpt) and stockwell (S-T) computational complexity?

What is computational complexity of continuous wavelet transform cwt ? What is computational complexity of wavelet packet transform ...
277 views

### Hints and helps to implement an accurate wavelet packet transfrom

I want to implement a Time-Freqency analysis by wavelet packets. I don't know what level and sampling rate should I use. I've tried different value for level(3,4,5,6,). but I couldn't get an accurate ...
576 views

### Instantaneous Frequency Estimation by Hilbert Transform - Theoretical Justification and Proof

I would like to better understand why the instantaneous frequency estimation by Hilbert transformation works (and especially why it doesn't work / lead to precise results in many cases). The ...
1k views

### How to interpret the effect of different windows in short time fourier transform?

There are many categories of windows, e.g., rectangular, Gaussian, and triangular. What are their effects on STFT?
4k views

### Time-frequency representation of sound signal using Matlab

I am currently doing a project on sound signal processing by using MATLAB. I have a problem regarding creating the command line so that I can get a graph containing frequency by its time. But this ...
608 views

### Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)?

First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ...
253 views

### Infinite extent of spectrum, but also in time in Oppenheim's Discrete Time Signal Processing?

In Oppenheim's Discrete Time Signal Processing there's on p. 323 no limited band in both time and frequency - wouldn't that violate the Heisenberg Principle?
878 views

### Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain

My goal is to compute the Fourier of the product between two discrete time signals, y1 and y2. This can be done by computing the convolution between the fourier transform of y1, f1 and the fourier ...
485 views

### Confused on the difference between the frequency spectrum of an entire song, and the frequency spectrum of a point in time

I am very much a beginner in this field - but find it really interesting. However I am a little confused on a certain area of knowledge. If I have understood correctly: At any point in an audiosignal,...
385 views

### Time-Frequency Analysis of Big Data - Data Size Reduction: averaging the most appropriate method?

Explanation: I would like to analyse the data from an experiment, which investigates the performance of a mechanical component using sensors, that has generated 2000 CSV files. Each file contains 513 ...
58 views

Why are those two systems equivalent? System 1:$$\boxed{x[n]}\longrightarrow\boxed{\uparrow 3}\longrightarrow\boxed{\downarrow 4} \longrightarrow\boxed{y[n]}$$ System 2:$$\boxed{x[n]}\longrightarrow\... 2answers 267 views ### system response: time vs frequency. Why do I get different magnitudes? I am simulating a linear system described by the following equation m \ddot{x} + c \dot{x} + k x = A \sin(\omega t) ... 2answers 1k views ### Compensate for phase shift of Hilbert transform I'm using Octave and trying to use the "instfreq" function from the time frequency toolbox which requires an analytic signal input. To get this analytic signal I'm using the Octave function "hilbert" ... 2answers 1k views ### Time delay estimate and sampling frequency This is an extention to my other question. My sampling frequency is only about 2x my tone frequency. I want to estimate time delay of arrival using this signal. I am generating the tone signal so I ... 2answers 729 views ### Linear and Circular Convolution in Fourier Domain (DFT) Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ... 1answer 714 views ### About phase unwrapping I am not too familiar with phase-related problems so I need some suggestions or corrections in a problem that might be an old but easy one. Here is my problem: given a complex signal:$$y(t) = e^{j\...
Suppose we have two sequences $x[n]$ of length $L$ , and $y[n]$ of length $P$. If we are doing a $L$ length circular convolution between the two sequences ($L>P$), how many of the resultant samples ...