Limits of integer-length delay lines

At low frequencies (large $N$), this is less of a problem, but becomes increasingly problematic at higher frequencies when delay-line lengths are small and a single sample delay can make a bigger difference.

Figure 15: As the desired frequency gets higher, it is quantized to fewer possible values; there is a single frequency value for all desired frequencies between 7000 and 8000 Hz.

Example: at $f_s = 44100$,

• to obtain a frequency of 882 Hz, a delay of $f_s/882 = 50$ samples is required;
• the next highest possible frequency with an integer number of samples is $f_s/49 = 900$ Hz.