# Digital Audio: Part 12 - Sampling Rate Conversion

In real systems the issue of sampling rate conversion arises frequently but fortunately there are plenty of solutions.

Fig.1 - The easiest form of rate conversion is shown at a) in which the rate is changed by an integer, so samples at the lower rate always coincide in time with samples at the higher rate. Next hardest is b), in which a fractional relationship means that samples coincide periodically and a finite number of phases of conversion are needed. Hardest of all is c) where there is no relationship between the rates and an infinite number of phases is needed.

Fig.2 - At a) is a band limited audio waveform. At b) it has been sampled at a constant rate. At c) the same sampling rate was used, but with a different starting point. The entire waveform is stored in the samples of b) and the same waveform is stored in the samples of c). Even though the samples are all different, b) and c) sound exactly the same.

Fig.3 - A basic way of rate converting is to connect a DAC and an ADC in series as shown here. One of the low-pass filters is redundant. Modern convertors are so good this works surprisingly well. A sampling rate convertor is simply a digital simulation of this figure.

Fig.4 - A transversal or finite impulse response filter creates a sampled impulse response as the impulse shifts across the stages.

Fig.5 - A reduction in sampling rate by a factor of 2. Input data shift across the transversal filter at the high sampling rate, but an output sample is only calculated on every other input clock.

Fig.6 - Digital interpolation, where the values of samples halfway between existing samples are calculated. See text for details.

# Digital Audio: Part 16 - Filters, Direct Implementation

There are two approaches to digital filtering. One is to implement the impulse response directly. The other is to use recursion. Here we look at the direct implementation.

# Microphones: Part 5 - The Variable Directivity Microphone

The variable directivity microphone is very popular for studio work. What goes on inside is very clever and not widely appreciated.

# Digital Audio: Part 15 - Filters

Digital filters are ubiquitous. That has happened because they have significant advantages over the technology they widely replaced.

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