Low-Pass Filter Noise Reduction

Before constructing filters with different bandwidths, it is necessary to perform an Inverse Fourier Transform to convert the signal from the frequency domain back to the time domain. This step is crucial because filter construction and application typically occur in the time domain, and the Inverse Fourier Transform serves as one of the primary methods for converting frequency domain signals to time domain representations. The inverse transformation process involves decomposing the frequency domain signal into its constituent frequency components and applying Fourier transformation to each component to reconstruct the time domain signal. In practical implementation, this can be achieved using functions like numpy.fft.ifft() in Python or ifft() in MATLAB, which compute the inverse discrete Fourier transform efficiently. Once the time domain signal is obtained, filters with varying bandwidths can be constructed according to specific signal processing requirements. The filter design process typically involves selecting appropriate cutoff frequencies and filter types (such as Butterworth, Chebyshev, or elliptic filters) to achieve desired attenuation characteristics. For low-pass filter implementation, functions like scipy.signal.butter() can be used to design the filter, followed by scipy.signal.filtfilt() for zero-phase filtering application. The bandwidth selection directly impacts the trade-off between noise removal and signal preservation, where narrower bandwidths provide more aggressive noise suppression but may attenuate desired signal components.