The selection of filter cutoff frequency has many important impacts on signal processing. It is directly related to the quality of the signal, the performance of the system and the accuracy of the final processing results. The following is a detailed introduction:

1. Impact On Signal Component Retention:

The cutoff frequency determines the filter's ability to filter signal components of different frequencies. For low-pass filters, if the cutoff frequency is set too high, it may not be able to effectively filter out high-frequency noise, resulting in the output signal still containing more interference components, affecting the purity of the signal; if the cutoff frequency is set too low, it will over-attenuate the useful high-frequency components in the signal, causing the signal to be distorted. For example, in audio processing, the main frequency components of speech signals are generally between a few hundred hertz and a few thousand hertz. If the cutoff frequency of the low-pass filter is set too low, the high-frequency details in the speech (such as some consonant pronunciations) will be filtered out, affecting the clarity of the speech. For high-pass filters, if the cutoff frequency is too high, too many low-frequency useful signals will be filtered out; if the cutoff frequency is too low, low-frequency noise cannot be effectively removed.

2. Impact On Signal Bandwidth And Transmission Rate:

In scenarios involving signal transmission such as communication systems, the filter cutoff frequency is closely related to the signal bandwidth. The cutoff frequency of the bandpass filter determines the frequency range of the signal, that is, the signal bandwidth. If the cutoff frequency is not selected properly, the signal bandwidth may be too narrow, so that some frequency components of the signal cannot pass through, causing signal distortion, and also limiting the signal transmission rate; if the bandwidth is too wide, although the signal can pass completely, it may introduce more interference signals and reduce the system's anti-interference ability. For example, in wireless communications, if the cutoff frequency of the bandpass filter cannot accurately match the frequency band of the transmitted signal, it will affect the data transmission rate and accuracy.

3. Impact On System Response Speed:

The cutoff frequency affects the response speed of the filter. Generally speaking, a lower cutoff frequency means that the filter reacts more slowly to changes in the signal because it takes more time to process low-frequency signal components. In a control system, if the cutoff frequency of the low-pass filter that filters the sensor signal is too low, the system's response to changes in the input signal will be delayed, affecting the system's real-time performance and control accuracy. On the contrary, a higher cutoff frequency allows the filter to respond to signal changes more quickly, but it may reduce the ability to suppress noise.

4. Impact On System Stability:

In some complex signal processing systems, the selection of filter cutoff frequency may affect the stability of the system. For example, in a feedback control system, the filter is part of the system, and its cutoff frequency will affect the closed-loop transfer function and frequency characteristics of the system. If the cutoff frequency is not selected properly, the system may oscillate or become unstable. An inappropriate cutoff frequency may change the phase margin and gain margin of the system, thereby affecting the stability of the system.

5. Impact On Signal Spectrum Characteristics:

The selection of cutoff frequency changes the spectrum structure of the signal. The filter attenuates or retains different frequency components by setting the cutoff frequency, thereby changing the spectrum shape of the signal. For example, after being processed by a low-pass filter, the high-frequency spectrum components of the signal are attenuated, and the spectrum becomes more concentrated in the low-frequency band; after being processed by a band-pass filter, the signal only retains the spectrum components of a specific frequency band, and other frequency bands are suppressed. This change in spectrum characteristics will have an important impact on subsequent signal analysis and processing (such as spectrum analysis, feature extraction, etc.), and different cutoff frequency selections may result in different extracted signal features.