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When performing DSP algorithms data needs to be stored as it is being input. Only a certain amount of data is kept. New data is saved and the old data is removed. This is a first-in-first-out (FIFO) buffer. There are two ways to implenent the FIFO buffer. One is to shift the data and the other is to implement a circular buffer.
There are two ways of implementing a FIFO buffer. Both methods start with defining an array that is the length of data needed to be stored. The first method of implementing a FIFO buffer is to add the new data to the beginning of the buffer and shifting the old data in the buffer. The last value that is shifted out is discarded or used before it is removed.
To implement the FIFO buffer by shifting the following pseudo-code can be used.
N - number of coefficients
x(n) - stored input data, n = 0...N-1
input_sample - variable that contains the newest input sample
// Shift in the new sample. Note the data is shifted starting at the end.
for (i=N-2; i>=0; i--){
x[i+1]= x[i];}
x[0]= input_sample
The second method is the more preferable method since it takes less processing. In this method a circular buffer is implemented. An index keeps track of the current point in the buffer. The data in the buffer does not get shifted, the index gets incremented and wrapped around when it gets to the end of the buffer. The element after the current index is the last value in the circular buffer. The following figure shows the circular buffer after the index has already wrapped around.
In the following figure is an example of a FIFO circular buffer with the number elements equal to 7. In the figure the current index is 3 and that is where the new sample is stored. The last element in the buffer is in element 4.
When a new value is received, the index is incremented (and possibly wrapped around to zero), the old value where the index points can be saved in a temporary variable to be used later and the new value is written where the index points thus deleting the old value. After another increment the new representation of the data will look like the following figure.
In terms of signal processing notation, the value at the index 4 is x(n). Since the value at the index 3 came in one time sample before the index 4, it corresponds to x(n-1). Similarly, the value at index 2 is x(n-2).
The following code shows pseudo-code that can be used to implement a circular buffer.
N - number of coefficients
x(n) - stored input data, n = 0...N-1
input_sample - variable that contains the newest input sample
index - location in the buffer where the current sample is stored
index = (index+1)%N; // use the remainder to wrap around the index
x(index) = input_sample;
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