Basic Processing on Frequency

When talking about processing on frequency we need to understand first what digitizing a signal means and other basic concepts like: frequency or rate and the difference between analog signals and digital signals.

Digitizing a signal is a process in which a message or signal becomes a sequence of electronic pulses. These electronic pulses are binary code (0’s and 1’s) of which the analog signals consist of and they are called bits. This process consists in three parts: the sampling, the quantization and the codification.

The analog signals are always continuous, but when the message turns into digital signals it becomes a non-continuous signal. This happens because we only take little samples of the analog signal; therefore we can say that we lose information. The frequency or rate is the rhythm of the sampling and this rhythm is the one that defines the samples that are taken in a certain time. In conclusion, the higher sampling rate you have the better signal quality you will get. When digitizing the signal we need to consider some basic concepts like the ones below.

Resample

As we said before sampling would be the process of converting an analog signal into a digital signal. Resampling is a similar process that consists of converting a piece of digital audio into another piece of digital audio. Why would you want to do that? We usually use this process when we need to convert the file into a different format because for some reason we can’t play the original or because we need to compress it, for example.

The problem with this process is that we always end up losing quality of the signal as some of the information disappears. And that means we will never have the same quality again of that signal. It is also good to know that this process has many other names such as: sampling frequency conversion, unsampling, downsampling, upscaling or downscaling.

Aliasing

To understand the process of aliasing we need to refer first to the Nyquist-Shannon sampling theorem. This theorem basically says that the sampling rate must always be the double of the maximum audible frequency.

When the Nyquist criterion is not satisfied, adjacent copies overlap and we get the appearance of an incorrect lower frequency. Aliasing is used to avoid this problem, it is done by using a filter called antialiasing. Technically it filters the input to an ADC to remove frequencies above half the sampling rate.

aliasing_effects

The antialiasing is more common in computer’s graphics problems, in which we would be talking about pixels and it’s easier to understand visually like in the example we will find below.

antialias

Transposition and Pitch Bend

Transposition and Pitch Bend are two concepts that can to be explained together as they are very similar concepts that have a simple difference. Transposition is, as Wikipedia says:

“In music transposition refers to the process, or operation, of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant interval.”

The main difference between this concept and pitch bend is that this last one modifies the pitch just for a moment instead of the constant interval we were talking about before. Then, we would define pitch bend as a temporary modification of the pitch.

A clear example of transposition would be when we use a capo in a guitar to raise the pitch. Another example would be the one we have below that we find in the Wikipedia article about transposition, which also has the audible example here.

“The melody on the first line is in the key of D, while the melody on the second line is identical except that it is major third lower, in the key of B.”

And an example of pitch bend, when we use the program Auto-tune and we modify the pitch of the voice in a certain moment to correct it. Finally we have a video below explaining this last concept in detail.

In conclusion, we need to know four concepts related to basic processing on frequency. The first one, resampling, is converting a digital signal into a new digital signal. Related to the second concept, we need to know that, when sampling ,we always should avoid aliasing (sampling a function at two or fewer times per cycle leads to missed cycles) by using antialiasing filters. And the final two processes (transposition and pitch bend) help us create different effects in the signal or to change the pitch. This modification in the pitch can be temporary, and that would mean we are using the pitch bend; or it can be a modification by a constant interval, which would mean that we used the process of transposition.

Webgraphy

http://en.wikipedia.org/wiki/Digitizing

http://en.wikipedia.org/wiki/Sample_rate_conversion

http://en.wikipedia.org/wiki/Transposition_(music)

http://es.wikipedia.org/wiki/Aliasing

http://ti-me.org/members/october2002/pitchbend.html

http://www2.udec.cl/~lsalazarv/digitalizacion.html

http://es.wikipedia.org/wiki/Antialiasing

http://es.wikipedia.org/wiki/Teorema_de_muestreo_de_Nyquist-Shannon

PREZI PRESENTATION HERE

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