Filtering

What Is Filtering?

Filtering is spectral shaping. A filter changes the spectrum of a signal by

emphasizing or de-emphasizing certain frequency ranges.

Filter Types

Lowpass Highpass Bandpass Band RejectThey 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 Eliminates higher frequencies (it “lets the lows pass”)

LPF

Amp.Freq. White Noise(all frequencies at equal amplitude)

Input spectrum Amp.Freq.Output spectrum

1.0

0.707

A lowpass filter is characterized by its cutoff frequencyThe cutoff frequency is the point where the spectrum is 0.707 of its original amplitude.Recall: power is proportional to amplitude squared.0.7072 = 0.5 Therefore, the cutoff frequency is the half-power level, -3 dB.

Frequency response/

Lowpass Filter

Simple lowpass filterCutoff frequency oscillates between 400 Hz and 4000 Hz

White noise

Simple LPFWhite noiseRange is 0 - 10 kHzCenter frequency oscillates from 400 - 4000 HzDuration: 7.5 seconds

Lowpass Filter

Simple lowpass filterCutoff frequency oscillates between 400 Hz and 4000 Hz

Sawtooth wave

Simple LPFSawtooth wave - notice the harmonicsRange is 0 - 6 kHzCenter frequency oscillates from 400 - 4000 HzDuration: 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.

Amp.Freq.Output spectrum

Highpass Filter Eliminates lower frequencies (it “lets the highs pass”)

HPF

Amp.Freq. White Noise(all frequencies at equal amplitude)

Input spectrum

1.0

0.707

A highpass filter is also characterized by its cutoff frequency

Frequency response/

A Feedforward Highpass Filter

Simple HPF - white noiseCutoff frequency oscillates: 400 - 4000 HzDuration: 7.5 secRange: 0 - 6 kHz

Simple HPF - sawtoothCutoff frequency oscillates: 400 - 4000 HzDuration: 7.5 secRange: 0 - 6 kHz

Amp.Freq.Output spectrum

Bandpass Filter Creates a spectral peak (a band is allowed to pass)

BPF

Amp.Freq. White Noise(all frequencies at equal amplitude)

Input spectrum

1.0

0.707

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

Amp.Freq.Output spectrum

Band-Reject Filter Creates a spectral trough

BRF

Amp.Freq. White Noise(all frequencies at equal amplitude)

Input spectrum

1.0

0.707

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