What is Called a ‘System’ in Signal Processing?

A system takes an input signal x, processes it somehow, and produces an output signal y.

For instance, if we have a time-domain vibration signal from a sensor, we can apply the Fast Fourier Transform (FFT) to convert it into a frequency-domain signal. The output signal is a frequency spectrum that reveals the system's vibration characteristics.


A system has its own characteristics that define how it processes input signals and produces output signals. What are the most salient characteristics of a system?


·       Linearity: If you scale the input signal, the output signal scales proportionally. It follows the principle of superposition. If you have an input signal x1 that produces an output signal y1 and another input signal x2 that produces an output y2, then the combined input signal x1+x2 will produce an output signal y1+y2.

Example: If you pour twice the amount of water into a glass, the glass will contain twice the amount.

 

·       Time Invariance: This means that the response of a system does not change over time; it merely experiences a time shift equivalent to the input time shift. In other words, if the input signal is shifted in time, the output will be shifted by the same amount without altering its shape.



Example: If you play a song and pause it at specific points, the music itself doesn't change; it just experiences a time shift. When you resume playing, the song continues from where it left off, maintaining its original content and characteristics.


·         Causality: A system is causal if its output depends only on the current and past inputs and not on future inputs. In other words, the system's response is based on information that is available up to the present time.

Example: When you clap your hands, it creates vibrations in the air. This is a causal system because the sound (output) occurs only after the hands are clapped (input). The sound cannot happen before the clapping action.

 

·       Stability: A system is stable if a bounded input signal results in a bounded output signal. In other words, if the input signal remains within a specific range, the output signal should also stay within a finite range and not grow without bounds.

Example: If you input a signal that stays between -1 and 1, the output should remain within some fixed range and not grow uncontrollably.

 

 

Comments

Post a Comment

Popular posts from this blog

The Importance of Understanding Elemental Signals

Image
Elemental Signals are fundamental components of complex signals, which are often decomposed into more straightforward signals (like sine waves).  By doing so, the analysis and manipulation of complex signals would be easier. Breaking down these signals into elemental components makes it easier to understand their characteristics, like frequency, amplitude, and phase. By identifying the elemental components of complex signals containing noise, we can easily apply some filtering and filter the noise out of signals. By doing so, we can decompose signals and have a modified version.  By reaching elemental signals, we can follow their frequency patterns, which can help in signal processing. Elemental signals include impulse, step, sinusoid, and Exposure signals.  An impulse signal (delta function) is a non-periodic signal that is zero everywhere except at a single point, where it has an infinite amplitude and zero duration. We have this signal when we have a s...
Read more

What is Random Noise?

Image
Random noise is an unwanted disturbance or random signal that interferes with a desired signal, making it harder to process or interpret. For example, in a phone call, your voice is the desired signal, while background noise like traffic or wind is a form of noise that can make the conversation harder to hear. Why is it called random noise? It’s because its values change randomly over time without any deterministic or repeating behavior. Random noise is not typically considered an elemental signal because it is not used to analyze or decompose other signals. Instead, it is usually something that needs to be filtered or minimized. The energy distribution across frequencies determines the " color " of noise. For instance, you may have heard of " white noise ". In white noise, the energy is equally distributed across all frequency bins, meaning it has constant energy at all frequencies. On the other hand, in pink noise , the energy decreases as ...
Read more