Signal
A signal is simply a series of numbers (e.g. [3, 4, 6, 2, 4] is a signal!). Typically these numbers represent a voltage that changes with respect to some physical phenomenon. When the voltage signal changes in time, it’s called a time series signal. Signal processing helps us analyze this sequence of numbers so we can learn more about the physical phenomenon it represents
This signal is also periodic, meaning that it repeats itself over and over again. The period is the amount of time it takes to make one repetition, which in this case is half a second. The frequency is the inverse of the period, or the number of repetitions per second, which is 2 hertz (Hz).
The last property of a periodic signal is the phase shift, which is similar to a time shift. If two signals are time shifted by one full period, there is no difference between them. For this reason, we express this shift by the fraction of the period that they are shifted. If a signal is shifted by a quarter of a period, we can say the phase shift is 90 degrees (360 being a full period). You can also measure phase shift in radians and there are 2 pi radians in a full period. So this phase shift would be half pi radians.
Digital sampling
The goal of digital sampling is to take an analog continuous-time signal, typically a voltage, and to quantize it and discretize it in time so that we can store it in a finite amount of memory and use the magic of computers to process it. The component that does this is called an analog-to-digital converter or an ADC, this is an example of a transducer. It is important to learn about the few fundamental ways the ADC changes the analog signal. In our head, it’s easy sometimes to pretend that we’re dealing with an ideal analog signal, but this can get us into trouble, and it’s important to know more detail about how signals are sampled to avoid pitfalls later on.
An ADC encodes a range of physical values to a set of discrete numbers. In this example, the analog signal varies over time between -3V and +3V and we are using a 4-bit ADC, which means that the ADC has 4 bits to encode the range from -3 to +3 (ie. the bit-depth of our sensor is 4). The 4 bits indicate that there are 16 discrete values and we can see the effect of this quantization in the digitized signal.
Vocabulary
- Period: The amount of time it takes to make one repetition.
- Frequency: The amount of repetitions in a given time period, usually 1 second is the time period.
- (Hz): The units of the sampling rate. 1Hz means 1 sample per second.
- Phase Shift: The shift between two similar periodic signals expressed in fractions of a period (multiplied by 2𝛑 radians or 360°).
- Transducer: Part of a sensor that converts a physical phenomenon into an electrical one (e.g., voltage)
- Analog-to-Digital Convert (ADC): A device (usually embedded in the sensor) that converts an analog voltage into an array of bits.
- Bit depth: The number of bits an ADC uses to create a sample. A 16-bit ADC produces a 16-bit number for each sample.
- Noise floor: The total amount of noise in the sensor, including electrical interference from the environment and other parts of the device, thermal noise, and quantization noise.
- Dynamic range: The physical range of the sensor. Values outside of this range will show up as clipping in the digital signal.
- Sampling rate: The frequency at which a sensor measures a signal.