Signals, Sample Rate and Resolution - What Does All This Stuff Mean Anyway?
You've probably come across the terms signal, sample rate and resolution, and you might have some understanding of their meaning. But what do they really mean? In this article, we'll walk you through the meaning of each of these technical audio terms.
What is a Signal?
The first thing to understand is what a signal is, at least in the context of taking acoustic measurements. The signals we are interested in are sounds recorded through a microphone or SPL (Sound Pressure Level) meter. The sound pressure generates electrical signals in the mic/meter which are captured by our audio interface. The interface takes measurements of the electrical level at its input.
What is a Sample?
Each measurement is referred to as a sample. How often it takes its samples is controlled by the sample rate.
REW supports a range of sample rates depending on the capabilities of the interface, common rates are 44.1kHz or 48kHz – which means the interface is capturing the level at its input either 44,100 or 48,000 times every second. Three seconds of a signal sampled at 48kHz means a sequence of 3*48,000 = 144,000 measurement values. The highest frequency that can be captured at any given sample rate is half the rate – we need at least two samples for each cycle of the frequency to reproduce it. At 48kHz sampling that means the highest frequency we can capture is 24kHz. Frequencies higher than half the sample rate would cause aliasing, they would appear to be lower than they actually were. For example, a 25kHz signal sampled at 48kHz would actually look like a 23kHz signal. To prevent this, the inputs of the interfaces have anti-aliasing filters that try to block signals higher than can be captured, but they are not completely effective so we always need to consider the frequency content of the signals we are trying to capture.
The resolution of the interface measurements is typically either 16 bits or 24 bits. 16 bit resolution is the same as used on CDs, and is the resolution REW supports. Having 16 bit resolution means the individual measurement values can range from -32768 to +32767 (numbers that can be represented with 15 binary digits, plus a 16th binary digit to store the sign of the number). Rather than use the measurement numbers directly, it is convenient to refer to them in terms of how close they are to the largest number, which is referred to as Full Scale and abbreviated as FS. The full scale values are -32768 and +32767. The smallest non-zero measurement value is 1, which as a percentage of full scale is 100*(1/32768) or approximately 0.003% FS. Anything smaller than that is seen by the interface as zero. The full scale value will correspond to a certain voltage at the interface input – that is usually around 1 Volt. Soundcards that have higher resolution, such as 24 bit, usually have the same maximum input voltage (around 1 Volt) but can use a wider range of numbers to measure the voltage. For a 24-bit interface the full scale measurement values are -8388608 and +8388607. That still is only 1 Volt (typically), the largest input voltage has not changed, but the 24-bit interface has higher resolution – the smallest value it can detect is 100*(1/8388608) percent of full scale, 0.000012% FS. It is with the very smallest signals that higher resolution has benefits. The full scale value is often treated as corresponding to a value of one, and everything below full scale as being the corresponding proportion of one, so half full scale would be 0.5 and so on.
