Fast Fourier Transform (FFT)
- The Fourier transform is a mathematical tool used to decompose a signal into its constituent frequencies.
- In Python, the Fourier transform can be computed using libraries like NumPy.
- The resulting spectrum represents the frequency content of the signal.
Analyzing the frequencies present in a musical note:
The below code generates a musical note signal with added noise, then applies Fast Fourier Transform (FFT) to analyze its frequency spectrum. The resulting plot displays the amplitude of frequency components present in the signal. Peaks in the plot represent dominant frequencies, indicating the note’s fundamental frequency and harmonics. The noise introduces additional frequency components, visible as smaller peaks or fluctuations in the plot.
import numpy as np
import matplotlib.pyplot as plt
# Generating a sample musical note signal
fs = 1100 # Sampling frequency (Hz)
duration = 2 # seconds
frequency = 440 # A4 note frequency (Hz)
t = np.linspace(0, duration, int(fs * duration), endpoint=False)
signal = np.sin(2 * np.pi * frequency * t) + np.random.normal(0, 1, len(t)) # Signal with noise
# Applying FFT
fft_result = np.fft.fft(signal)
freq = np.fft.fftfreq(t.shape[-1], d=1/fs)
# Plotting the spectrum
plt.plot(freq, np.abs(fft_result))
plt.title('FFT of a Musical Note')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Amplitude')
plt.show()
Output:
Significance of Fast Fourier Transform (FFT) in Spectrum Analysis:
FFT enables the efficient analysis of frequency components in signals, crucial for applications in music, communications, and more. The graph clearly indicates the presence of a dominant frequency, which corresponds to the musical note being played.
Spectrum Analysis in Python
Spectrum analysis is a powerful technique used in signal processing to analyze the frequency content of signals. It finds applications in various fields such as telecommunications, audio processing, and vibration analysis. In this article, we’ll explore the fundamentals of spectrum analysis and how it can be implemented in Python.
Table of Content
- What is Spectrum Analysis?
- Types of Spectrum Analysis
- Principles of Spectrum Analysis
- How to do Spectrum Analysis?
- 1. Fast Fourier Transform (FFT)
- 2. Power Spectral Density (PSD)
- Applications of Spectrum Analysis