Low-Pass Filter

A low-pass filter (LPF) is a basic type of spectral effect. It reduces the amplitude of high frequencies, but allows the low frequencies to pass through. Studying how a LPF works and how it is implemented provides a foundation for learning about all types of spectral effects.

The simplest digital LPF uses 1 sample of delay. By using the delay in parallel with a dry (unprocessed) signal, an interesting thing happens when the two paths are combined.

By having two signals which get combined together at the output, we have set up “interference.” For high frequencies, this introduces destructive interference and the combined amplitude is decreased at the output. For low frequencies, there is constructive interference and the combined amplitude is increased.

This is because the 1-sample delay introduces a large phase shift ( $\sim 180^{\circ}$ ) compared to the dry path for high frequencies. When two signals are added together with a 180 degree phase difference, their amplitude cancels.

However, the 1-sample delay introduces a negligible phase shift ( $\sim 0^{\circ}$ ) for low frequencies. When two signals are added together with no phase difference, their amplitude increases.

There is a built-in Matlab function which can be used to analyze the frequency response of any spectral filter. The function analyzes the impulse response of the filter, h. The syntax to use the function is freqz(h). It creates a plot of the magnitude (amplitude) response and the phase response of the filter.

Next, let’s look at another type of spectral effect: the high-pass filter.