DSP Project 2  

Audio Special Effects
By Anthony Staiano
a) Audio Equalizer
b) Artificial Reverb

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First I needed to create an 8-band Graphical User Interface for the audio equalizer. Each of the 8 bands were controlled by a slider that would linearly vary from +10dB to -10 dB. The 8 different frequency bands that I had to account for were as follows:

Band #	Low Frequency (Hz)	High Frequency (Hz)
1	0	200
2	200	400
3	400	800
4	800	1,600
5	1,600	3,200
6	3,200	6,400
7	6,400	12,800
8	12,800	22,050

Next I designed an ideal linear phase FIR filter. This ideal linear phase FIR filter would give a model to design the actual FIR filter by the use of a window function.

For the graphic equalizer I needed to complete the following steps:


a) Acquire the 8 equalizer band settings.
b) Use the slider settings to create an ideal filter response.
c) Create a realizable filter by the use of a window function.
d) Apply the realizable filter to the audio input.

I decided to limit myself to a 256 tap FIR filter. This would allow me to implement the filter by the use of a single standard DSP chip. This would decrease my costs, (one chip vs. two chips).

Then I needed to pick which window function I would use in my filter design. I experimented with numerous window functions, including Bartlett, Blackman, Chebychev, Hamming, Hanning, and Kaiser. After all was said and done, I found that the Kaiser window gave the best results, when compared to the ideal plot. For all the other windows that I tried, (except for Blackman), I found that there was to much ringing for audio. Upon closer examination I found my best results were obtained for the Kaiser window with beta=9. (Both the kaiser window plot and ideal plot were for an arbitrary band equalizer.)

Finally, to prevent the possibility of signal clipping due to over amplification, the signal was normalized and then multiplied by the max value.

Sample Audio Sounds:

Here are a few examples of my equalizer at work, I used two different signals:


a) Metallica: "Mama Said", off there album Load.
b) Van Halen: "Hot For Teacher", off there album 1984.

Part b) Artificial Reverb Generator:

RD & RT:

When looking to design an artificial reverberation generator you need to look at the 2 important properties, RD and RT. RD, the reverberation density, is a measure of the number of echos per second. RT, the reverberation time, is the time is takes the energy to decay to -60dB. By varying these two values, (RD & RT), one can get the type of reverberation that you are looking. Since I know that the first 160ms of decay will give an inclination to the value of RT, I split the filter into a sum of a FIR Filter, and an IIR Filter as follows:


The first 160ms above will be designed by a FIR Filter, for the important early echos, and 160ms to RT will be designed by an IIR Filter, for the not so important later echos.

Reverb Design:

First I need to create a Graphical User Interface so the values of RT and RD could be easily changed. Both RT and RD were controlled by sliders. RD could vary from 10 to 1000 (log scale) , and RT could vary from 0 to 5 seconds.

Next I needed to find the decay constant for the exponential. With X as the original signal, and a value of zero at -60dB, or .001*X, must do is solve the following equation:

.001*X=X*e^(a/RT)

Solving this equation produces a=-6.9/RT. Using this value, along with the notion that the FIR part will last 160ms, (.16 frequency samples), one can create the equation for the output of the FIR Filter Yf, (see rev.m).

Now we need to create the IIR part. Since I already know the decay rate of the signal is, (see above), I must shift my IIR filter 160ms to the right to account for it starting at 160ms, not at zero, (again see rev.m).

Finally I added together my FIR and IIR parts to come up with my combination filter.

Sample Audio Sounds:

Here are a few examples of my reverb generator at work, I used two different signals, (both are sound bites from CaddyShack the movie).

a) Audi: Judge Smails is mad because someone in in his spot.
b) Laugh: Judge Smails and others laughing away.