
Sampling rate

In the separate article “Bit rate and bus width” and “Notes on reducing the bit rate”, we presented the history of the “bit rate”, which is the vertical axis of graph paper during PCM sampling.

This section considers the “sample rate” of the horizontal axis.
Maximum frequency that can be sampled (Nyquist frequency)
With the PCM method, exactly half the sample rate is the maximum recordable rate. This value is also called the “Nyquist frequency”.
For CDs recorded at a sampling frequency of 44.1 kHz, half, 22.05 kHz, is the theoretical maximum recordable frequency.
Now half the sample rate is the maximum recordable rate, and the reason is … Seeing is believing, see the figure to the right.
To represent a cycle of a sine wave, you must draw up and down round trips using at least two samples.
Alias noise: frequencies higher than recordable
But what if a signal with a frequency higher than the Nyquist frequency enters the A / D converter?
See the graphic to the right.
While the input signal performs “3 round trips with 4 samples”, the resolution of the horizontal axis (measurement frequency) of the A / D converter is too low to correctly follow the movement of the signal. The sampled values draw a “one round trip with four samples” waveform, which is significantly lower than the input frequency. Once again, the original signal is “manufactured” in the digital domain.
In this way, an input signal with a frequency higher than the Nyquist frequency is the source of a signal with a lower frequency than it should be, called “alias noise.”
Alias noise is also called “envelope noise” because it occurs at a frequency lower than the Nyquist frequency by the amount that the original signal exceeds the Nyquist frequency, as shown in the graph to the right. The alias noise that wraps around and reaches 0Hz continues to be wrapped between 0Hz and the Nyquist frequency so that it is reflected back.
Actually, the A / D converter contains a low pass filter to prevent such alias noise, so alias noise is not a problem when recording analog signals.
However, handling alias noise can be important when using plugins. The next section explains this point.
Do you need a high sample rate?
When starting to record or compose with a DAW, how to set the sample rate of the project is a difficult place. Unlike the bitrate above, once the sample rate is set, it is difficult to change it later.
It is generally said that the higher the sample rate, the higher the quality of the master that can be produced without damaging the original sound, but the PC specs required during work will also improve dramatically.
But is there any merit in editing at a high sample rate, like when the final medium is a 44.1 kHz CD? Also, can you ignore the difference in sample rate based on the trend of the sound you are looking for, such as the genre you are dealing with?
The bottom line is that when you use harmonic effects like saturators and compressors in your DAW, the sample rate setting can have a significant effect.
Next, we’ll use an ultrasound to consider how the project’s sample rate will change.
The first is a single scan signal sonogram. You can see that the frequency of the sine wave gradually increases from 0 to 22 kHz.
Let’s add a distortion effect to this.
In each case, the signal with the effect applied is exported in projects with different sample rates, and then the file is converted to 44.1 kHz.
All effects use the same preset.
Note that the files themselves that are comparing sonograms are all 44.1 kHz.


















