Page 1 Sampling theory Fourier theory made easy Page 2 Sampling theory Fourier theory made easy Sampling, FFT and Nyquist Frequency Page 3 Sampling theory Fourier theory made easy Sampling, FFT and Nyquist Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 5*sin (2 p4t) Amplitude = 5 Frequency = 4 Hz seconds A sine wave We take an ideal sine wave to discuss effects of sampling Page 4 Sampling theory Fourier theory made easy Sampling, FFT and Nyquist Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 5*sin (2 p4t) Amplitude = 5 Frequency = 4 Hz seconds A sine wave We take an ideal sine wave to discuss effects of sampling 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 5*sin(2 p4t) Amplitude = 5 Frequency = 4 Hz Sampling rate = 256 samples/second seconds Sampling duration = 1 second A sine wave signal and correct sampling We do sampling of 4Hz with 256 Hz so sampling is much higher rate than the base frequency, good Thus after sampling we can reconstruct the original signal Page 5 Sampling theory Fourier theory made easy Sampling, FFT and Nyquist Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 5*sin (2 p4t) Amplitude = 5 Frequency = 4 Hz seconds A sine wave We take an ideal sine wave to discuss effects of sampling 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 5*sin(2 p4t) Amplitude = 5 Frequency = 4 Hz Sampling rate = 256 samples/second seconds Sampling duration = 1 second A sine wave signal and correct sampling We do sampling of 4Hz with 256 Hz so sampling is much higher rate than the base frequency, good Thus after sampling we can reconstruct the original signal 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 sin(2 p8t), SR = 8.5 Hz An undersampled signal Undersampled signal can confuse you about its frequency when reconstructed. Because we used to small frequency of sampling. Nyquist teaches us what should be a good frequency Sampling rate Undersampling can be confusing Here it suggests a different frequency of sampled signal Red dots represent the sampled data Here sampling rate is 8.5 Hz and the frequency is 8 HzRead More

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