How to implement an Equalizer

Question

I know there are a lot of questions about equalizers in so, but I didn't get what I was looking. What I want to do is an equalizer for modifying audio samples in such a way like:

equalizer.eqAudio(audiosamples, band, gain)

I'm not sure if that is the exact interface that I want because I know little about DSP in terms of implementing them (I used filters, limiters, compressors but not made them).

So Googling about this I read that I must do a FFT to the samples so I get the data per frequency ranges instead of amplitude, process it the way I want and then make the inverse of the FFT so I get the result in audio samples again. I looked for an implementation of this FFT and found JTransform for Java. This library has an implementation of a FFT related algorithm called Discrete Cosine Transform (DCT).

My questions are :

• Well, Am I in the right way?
• Since FFT gives me data about frequency, I should pass to the FFT algorithm a chunk of samples. How big this chunk must be?
• Is there a good book about DSP programming that explains equalizers ?

Thanks!

Tokay

Answer 1

There are many different ways to obtain an equalizer, and as Shannon explains, the IIR/FIR filter way is one of them. However, if your goal is to quickly get an equalizer up and running, going the FFT way might be easier for you, as there exist a wealth of reference implementations.

As to your question of FFT size, it depends on what frequency resolution you want your equalizer to have. If you choose a size of 16, you will get 9 (8 complex + 1 real) channels in the frequency domain equally spaced from 0 to fs/2. The 1st is centered around 0Hz, and the 9th around fs/2 Hz. And note, some implementations return 16 channels where the high part is a mirrored and complex conjugated version of the low part.

As to the implementation of the equalizer functionality, multiply each channel with the wanted gain. And if the spectrum have the mirrored part, mirror the gains as well. If this is not done, the result of the following IFFT will not be a real valued signal. After multiplication, apply the IFFT.

As to the difference between a FFT and filter based equalizer, remember that a FFT is simply a fast way of calculating a set of FIR filters with sines as impulse, critically sampled (downsampled with the filter length) and evenly spaced center frequencies.

Regards

Believe

Answer 2

FFT wouldn't be my first choice for audio equalisation. I would default to building an EQ with IIR or FIR filters. FFT might be useful for special circumstances.

A commonly recommended reference is the Cookbook Formulae for Audio EQ Biquad Filter Coefficients.

A java tutorial for programming biquad filters. http://arachnoid.com/BiQuadDesigner/index.html

Is there a good book about DSP programming that explains equalizers ?

Understanding Digital Signal Processing is a good introduction to DSP. There are chapters on FIR and IIR filters.

Intoduction To Digital Filters with Audio Applications by Julius O. Smith III.

Graphic Equalizer Design Using Higher-Order Recursive Filters by Martin Holters and Udo Zolzer is a short paper detailing one EQ filter design approach.

Floppy

Holters ... link is gone – Lamont