Hi Prashanth,
I understand that you are willing to understand the computational duration when comparing ‘Fast Fourier Transform’ and ‘Wavelets’ both theoretically and programmatically .
Theoretical comparisons between FFT and Wavelets are as follows:
1. Frequency vs. Time-Frequency Analysis:
- FFT: Primarily for frequency analysis, transforms time-domain signal into frequency representation.
- Wavelets: Provides time and frequency localization, analyzing signal at different time intervals.
2. Resolution:
- FFT: Uniform frequency resolution, lacks time localization.
- Wavelets: Variable resolution in time and frequency, high for high-frequency components, low for low-frequency components.
3. Multiresolution Analysis:
- Wavelets support multiresolution analysis, analyzing signals at different scales or resolutions for detailed examination.
Refer to the below code snippet for better understanding :
% Generate a sample signal
fs = 1000; % Sampling frequency
t = 0:1/fs:1; % Time vector
f1 = 10; % Frequency of sinusoid 1
f2 = 50; % Frequency of sinusoid 2
x = sin(2*pi*f1*t) + sin(2*pi*f2*t);
% FFT
tic; % Start timer
X = fft(x);
fftTime = toc; % End timer
% Wavelet Transform
tic; % Start timer
wname = 'db4'; % Wavelet name (Daubechies 4)
level = 5; % Decomposition level
[C, L] = wavedec(x, level, wname);
waveletTime = toc; % End timer
% Display computational duration
fprintf('FFT duration: %.4f seconds\n', fftTime);
fprintf('Wavelet transform duration: %.4f seconds\n', waveletTime);
Documentation link for details : mathworks.com/help/wavelet/gs/from-fourier-analysis-to-wavelet-analysis.html
