Equalizers. Contents: IIR or FIR for audio filtering? Shelving equalizers Peak equalizers

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1 Equalizers 1 Equalizers Sources: Zölzer. Digital audio signal processing. Wiley & Sons. Spanias,Painter,Atti. Audio signal processing and coding, Wiley Eargle, Handbook of recording engineering, Springer Contents: Introduction IIR or FIR for audio filtering? Shelving equalizers Peak equalizers

2 1 Introduction Equalizers 2 Spectrum equalization is one of the basic operations of audio processing Equalizers can be found both in consumer products as well as in professional use Consumer products (e.g. car radio or amplifier) often employ simple bass and treble control Recording studios and professional audio often use more complex devices, for example equalizers with one-third octave filters Note about terms The reference textbook uses the terms recursive and non-recursive filter for IIR and FIR filters, respectively

3 2 IIR or FIR for audio processing? Equalizers 3 IIR filters are computationally more efficient Narrow transition band is achieved using a small number of filter coefficients (multiplication operations) FIR filters enable linear phase response = Filtered signal is a delayed version of the original at the passband In the case of audio that is not always important, since the human ear is not very sensitive to frequency component phases Magnitude response is perceptually more important à supports choosing IIR filters Phases at low frequencies affect the stereo image In audio processing, there are some signals where retaining the waveform shape (i.e., phase reponse) is important: for example amplitude envelope as a function of time

4 Equalizers 4 IIR or FIR for audio processing? FIR filters allow more accurate control of the filter response When designing filterbanks, FIR filters enable so-called perfect reconstruction, meaning that analysis/synthesis filterbank does not distort the signal if no processing is done at the subbands Simplifies the design of an audio codec, for example (most use FIR filterbank) Varying the filter response in real time (for example varying the cut-off frequency) is easier with IIR filters Parametric filter structures, tables of parameter values available for different types of operations. One advantage of FIR filters is their granted stability and usually shorter required wordlength when quantizing the filter coefficients and state à Choice FIR / IIR depends on the application

5 3 Shelving equalizers (IIR) Equalizers 5 Shelving equalizers (shelving filters) are used to boost or cut certain frequencies A given frequency band is weighted (boost: > 1, cut: < 1) Unlike filters which aim to remove or certain frequencies Idea: Change the gain of some part of the spectrum while leaving other parts untouched Application to equalization is obvious Manipulating the system frequency response only at a given frequency range

6 First order shelving filter design Equalizers 6 A low-pass shelving filter can be expressed as " 1 b H lp (z) = C 1 z 1 % lp $ ' # 1 a 1 z 1 & 1+ kµ 1 kµ 1 k C lp =, b1=, a1= 1+ k 1+ kµ 1+ k, k = 4 1+ µ tan " Ω % c $ ',µ =10 G/20 # 2 & A high-pass shelving filter " 1 b H hp (z) = C 1 z % 1 hp $ ' # 1 a 1 z 1 & C hp = 1+ p 1+ p, b1= µ p 1 p, a1= µ + p 1+ p, k = " 4 % $ ' # 1+ µ & where G is gain (db) and Ω c is normalized cutoff frequency. 1 " tan Ω % c $ ',µ =10 G/20 # 2 &

7 Equalizers 7 6 db Low-Pass shelving filter responses

8 Shelving filters (IIR) Second-order shelving equalizers Equalizers 8 Figure: magnitude responses of second-order shelving filters Boost/cut of low frequencies: f c = 100 Hz Boost/cut of high frequencies: f c = 5000 Hz In some equalization applications, steep transition bands are not desired, but for example smooth boost or cut towards low frequencies, starting at a given cutoff frequency

9 Feed forward / backward structure for implementing shelving filters Equalizers 9 Consider the forward (= boost) case first: Consists of a high-/low-/bandpass filter H(z) and and all-pass component Transfer function G FW ( z) = 1+ H0H( z) In the cut case: 1 G FB ( z) = 1+ H H( H 0 determines amount of boost or cut H(z) can be low-, high-, or bandpass filter (any filter basically) For example for boosting low frequencies, H(z) is a lowpass filter and the gain at zero frequency will be V 0 = 1+H 0 Note that G FW (z) (boost) and G BW (z) (cut) in a cascade will cancel out each other and lead to unity gain at all frequencies In Feed backward case the transfer function has to take the form 1 to be stable (feedback without delay is not allowed) H ( z) = z H1( z) 0 z )

10 Peak filter Equalizers 10 The transfer function of a peak equalizer " 1+ b H pk (z) = C 1 z 1 + b 2 z 2 % pk $ ',C # 1+ a 1 z 1 + a 2 z 2 pk = 1+ k qµ " 4 % ", k q = $ 'tan Ω % c $ ' & 1+ k q # 1+ µ & # 2Q & b 1 = 2cos(Ω c ) 1+ k q µ, b 2 = 1 k qµ 1+ k q µ, a 1 = 2cos(Ω c ) 1+ k q, a 2 = 1 k q 1+ k q, where Q is quality factor, G is gain (db) and Ω c is normalized cutoff frequency.

11 Equalizers 11 Creative use of equalizers Instead of fixing a problem, creativeness can be expressed with equalizers Fullness: adding +4 to +6dB Hz range to emphasize weak instruments (e.g. acoustic guitar, harp) Crispness: for percussion instruments by adding HF shelving boost above 1-2 khz. Emphasize articulation transients of instruments. E.g. boost frequencies of finger movements on string instruments.

Phase Correction System Using Delay, Phase Invert and an All-pass Filter

Phase Correction System Using Delay, Phase Invert and an All-pass Filter University of Sydney DESC 9115 Digital Audio Systems Assignment 2 31 May 2011 Daniel Clinch SID: 311139167 The Problem Phase is