Filtering

What Is Filtering? n Filtering is spectral shaping. n A filter changes the spectrum of a signal by emphasizing or de-emphasizing certain frequency ranges.

Filter Types n Lowpass n Highpass n Bandpass n Band Reject They are characterized by their frequency responses. This is a graph showing how they shape the spectrum of a noise signal (all frequencies at equal amplitude).

Lowpass Filter n Eliminates higher frequencies (it “lets the lows pass”) LPF A lowpass filter is characterized by its cutoff frequency The cutoff frequency is the point where the spectrum is of its original amplitude. Recall: power is proportional to amplitude squared = 0.5 Therefore, the cutoff frequency is the half-power level, -3 dB. Frequency response/

Lowpass Filter Simple lowpass filter Cutoff frequency oscillates between 400 Hz and 4000 Hz White noise Simple LPF White noise Range is kHz Center frequency oscillates from Hz Duration: 7.5 seconds

Lowpass Filter Simple lowpass filter Cutoff frequency oscillates between 400 Hz and 4000 Hz Sawtooth wave Simple LPF Sawtooth wave - notice the harmonics Range is kHz Center frequency oscillates from Hz Duration: 7.5 seconds

Lowpass Filter Lowpass filters are an essential component in the design of digital recorders. An audio signal must be lowpass filtered before it is sampled to eliminate frequencies above the Nyquist frequency.

Highpass Filter n Eliminates lower frequencies (it “lets the highs pass”) HPF A highpass filter is also characterized by its cutoff frequency Frequency response/

A Feedforward Highpass Filter Simple HPF - white noise Cutoff frequency oscillates: Hz Duration: 7.5 sec Range: kHz Simple HPF - sawtooth Cutoff frequency oscillates: Hz Duration: 7.5 sec Range: kHz

Bandpass Filter n Creates a spectral peak (a band is allowed to pass) BPF A bandpass filter is characterized by center frequency and bandwidth. The bandwidth is the distance between points on either side of the center frequency where the power drops 3 dB. CF BW Bandwidth filters are also described by Q (quality), which is the center frequency over the bandwidth (CF/BW). Q is generally a more useful description than simple bandwidth. Frequency response/

Bandpass Filters Fixed Q, Center Frequency oscillates between 400 Hz and 4000 Hz Fixed Center Frequency, Q value oscillates White noise

Bandpass Filters Fixed Q, Center Frequency oscillates between 400 Hz and 4000 Hz Fixed Center Frequency, Q value oscillates Sawtooth

Band-Reject Filter n Creates a spectral trough BRF A band reject filter is characterized by center frequency, bandwidth and Q. Band reject filters are less common than the other three types. CF BW Frequency response/

Band Reject Filters Fixed Q, Center Frequency oscillates between 400 Hz and 4000 Hz Fixed Center Frequency, Q value oscillates White noise

Band Reject Filters Fixed Q, Center Frequency oscillates between 400 Hz and 4000 Hz Fixed Center Frequency, Q value oscillates Sawtooth