【Practical Exercise】Time-Frequency Analysis of Signals Using MATLAB

发布时间: 2024-09-14 06:45:47 阅读量: 70 订阅数: 85
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# 2.1 Principles and Methods of Time-Frequency Analysis Time-frequency analysis is a technique that represents signals simultaneously in the time and frequency domains. It reveals the frequency components of a signal that change with time, providing a more comprehensive perspective for signal analysis and processing. ### 2.1.1 Short-Time Fourier Transform (STFT) STFT is a classical method for time-frequency analysis. It divides the signal into a series of overlapping time windows and then performs a Fourier transform on each window. By connecting the spectra of each time window, the time-frequency distribution of the signal is obtained. ```matlab % Signal x = sin(2*pi*100*t) + sin(2*pi*200*t); % STFT [S, F, T] = spectrogram(x, 256, 128, 512, 1000); % Plotting time-frequency distribution surf(T, F, abs(S), 'EdgeColor', 'none'); xlabel('Time (s)'); ylabel('Frequency (Hz)'); zlabel('Magnitude'); ``` # 2. MATLAB Time-Frequency Analysis Toolbox ### 2.1 Principles and Methods of Time-Frequency Analysis Time-frequency analysis is a powerful technique in signal processing used to analyze the time-frequency characteristics of signals. It decomposes signals into a joint representation of time and frequency, thereby revealing hidden patterns and trends in the signal. #### 2.1.1 Short-Time Fourier Transform (STFT) STFT is one of the most commonly used methods in time-frequency analysis. It divides the signal into a series of overlapping windows and then applies a Fourier transform to each window. This results in a time-frequency diagram, where the time axis represents the window position, and the frequency axis represents the frequency components of the Fourier transform. ```matlab % Import signal x = load('signal.mat'); % Set STFT parameters windowSize = 256; overlap = 0.5; % Calculate STFT [S, F, T] = spectrogram(x, windowSize, overlap); % Plot time-frequency diagram imagesc(T, F, abs(S)); colorbar; title('STFT Time-Frequency Diagram'); xlabel('Time'); ylabel('Frequency'); ``` #### 2.1.2 Wavelet Transform The wavelet transform is a multi-scale analysis technique that decomposes signals using a set of basis functions called wavelets. Wavelets have localization properties, which enable them to capture transient and non-stationary features of a signal. ```matlab % Import signal x = load('signal.mat'); % Set wavelet parameters waveletName = 'db4'; scales = 1:10; % Calculate wavelet transform [C, L] = wavedec(x, scales, waveletName); % Plot wavelet coefficient graph figure; for i = 1:length(scales) subplot(length(scales), 1, i); plot(C{i}); title(['Wavelet Coefficient Graph: Scale', num2str(scales(i))]); end ``` #### 2.1.3 Hilbert-Huang Transform (HHT) HHT is a nonlinear time-frequency analysis method that decomposes signals into a series of components called intrinsic mode functions (IMFs). IMFs are localized and represent different frequency components in the signal. ```matlab % Import signal x = load('signal.mat'); % Calculate HHT imfs = emd(x); % Plot HHT time-frequency diagram figure; for i = 1:length(imfs) subplot(length(imfs), 1, i); plot(x, imfs{i}); title(['Intrinsic Mode Function: ', num2str(i)]); end ``` # 3. MATLAB Time-Frequency Analysis Practice ### 3.1 Time-Frequency Feature Extraction of Signals #### 3.1.1 Power Spectral Density (PSD) The power spectral density (PSD) is a function that describes how signal power is distributed across frequencies. It can reveal the spectral characteristics of a signal and is used to identify periodic components and noise in a signal. **Calculation Method:** ```matlab % Signal x x = randn(1000, 1); % Calculate PSD psd = pwelch(x, [], [], [], 1024); % Plot PSD figure; plot(psd); xlabel('Frequency (Hz)'); ylabel('Power Spectral Density'); title('Power Spectral Density of Signal'); ``` **Logical Analysis:** * The `pwelch` function calculates the PSD of a signal, where: * `x`: Input signal * `[]`: Specifies the use of the default window size * `[]`: Specifies the use of the default overlap rate * `[]`: Specifies the use of the default sampling rate * `1024`: Specifies the frequency resolution of the PSD #### 3.1.2 Time-Frequency Distribution (TFD) The time-frequency distribution (TFD) is a function that describes the energy distribution of a signal on the time-frequency plane. It can reveal the time-varying characteristics of a signal and is used for analyzing transient and non-stationary signals. **Calculation Method:** ```matlab % Signal x x = chirp(0:0.001:10, 0, 1000, 2000); % Calculate time-frequency distribution (using STFT) tfd = spectrogram(x, 256, 128, 512, 1000); % Plot time-frequency distribution figure; imagesc(tfd); xlabel('Time (s)'); ylabel('Frequency (Hz)'); title('Time-Frequency Distribution of Signal'); ``` **Logical Analysis:** * The `spectrogram` function calculates the time-frequency distribution of a signal, where: * `x`: Input signal * `256`: Specifies the window size * `128`: Specifies the overlap rate * `512`: Specifies the frequency resolution * `1000`: Specifies the sampling rate #### 3.1.3 Coherence Coherence is a function that describes the correlation between two signals. It can reveal the similarity and time-frequency relationship between signals. **Calculation Method:** ```matlab % Signals x and y x = randn(1000, 1); y = randn(1000, 1); % Calculate coherence coh = mscohere(x, y, [], [], [], 1000); % Plot coherence figure; plot(coh); xlabel('Frequency (Hz)'); ylabel('Coherence'); title('Coherence between Signals'); ``` **Logical Analysis:** * The `mscohere` function calculates the coherence of signals, where: * `x`: Input signal 1 * `y`: Input signal 2 * `[]`: Specifies the use of the default window size * `[]`: Specifies the use of the default overlap rate * `[]`: Specifies the use of the default sampling rate * `1000
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