Project Title

Variable Bandpass Filter

In this project a tuning fork recording will have noise added to it, and the noise should subsequently be cleaned through digitial filtering. The main undertaking in this project is the filter design process. The filter design consideration will be justified here briefly, and the implementation can be seen below, and in the accompanying functions.

By taking the Fourier transform of the tuning fork recording it can be seen that the maximum frequency component Fm = 466 Hz, see the plot generated by the analyzeAudio function call in 1.1. This 466 Hz frequency is identical to the tuning for label. Knowing the frequency that needs to be isolated, the design process can begin.

Design Principles

The general steps of filter design are:

1. Choosing a windowing function. In the project, a Kaiser window was chosen as it provides an effective way of tailoring the response of the filter by adjusting the alpha parameter and the low pass cut-off frequency.
2. Chosing the filter parameter M, such that the transition band is less than or equal to the stop frequency minus the pass frequency (dF <= Fstop - Fpass).
3. Choose a cut-off frequency Fc for the truncated impulse response such that Fc = (Fstop + Fpass)/2.
4. Plot the frequecy magnitude to see resulting filter satisfies the desired criteria.
5. Adjust Fc and M to meet desired response. M should be minimized as computationally heavy to have large values of M.

We are choosing a Kaiser window for easy filter tuning. The Kaiser window is calculated in 1.2 through a function call to kaiserLPF. The intent here is to use two Kaiser bandpass filters of different alpha parameters to first maximize stopband attenuation, and then use a narrow transition to clean up the signal. Then we will choose alpha1 = 7 for a large attenuation, and then alpha2 = 0, for a sharp transition.

For the filter parameter M should allow for the smallest possible transition band. Since the ideal frequency is 466 Hz, and the intent is to use a shifted low-pass filter, the cut-off frequency should be as small as reasonably possible. However, the smaller Fc is chosen, the greater the overattenuation of our desired signal occurs. We will start with an Fc value of 10, and adjust it experimentally. Then lets select parameter M for a 50 dB attenuation which is approximately 30.