Discrete-time signals are mathematical entities; in particular, they are functions with an independent time variable and a dependent variable that typically represents some kind of real-world quantity of interest. But as interesting as a signal may be on its own, engineers usually want to
do something to it. This kind of action is what discrete-time systems are all about. A
discrete-time system is a mathematical transformation that maps a discrete-time input signal (usually designated $x$) into a discrete-time output signal (usually designated $y$). In other words, it takes an input signal and modifies it to produce an output signal:
System $\mathcal{H}$ takes takes a discrete time signal $x$ as an input and produces an output $y$. There is no end to the possibilities of what a system could do. Systems might be trivially dull (e.g., produce an output of 0 regardless of the input) or incredibly complex (e.g., isolate a single voice speaking in a crowd). Here are a few examples of systems:
A speech recognition system converts acoustic waves of speech into text
A radar system transforms the received radar pulse to estimate the position and velocity of targets
A functional magnetic resonance imaging (fMRI) system transforms measurements of electron spin into voxel-by-voxel estimates of brain activity
A 30 day moving average smooths out the day-to-day variability in a stock price
Signal length and systems
Recall that discrete-time signals can be broadly divided into two classes based upon their length: they are either infinite length or finite length (and recall also that periodic signals, though infinite in length, can be viewed as finite-length signals when we take a single period into account). Likewise, discrete-time systems are also finite or infinite length, depending on the kind of input signals they take. Finite-length systems take in a finite-length input and produce a finite-length output (of the same length), with infinite-length systems doing the same for infinite-length signals.
Examples of discrete-time systems
So a system takes an input signal $x$ and produces an output signal $y$. How does this look, mathematically? Below are several examples of systems and their mathematical expression:
Identity: $y[n] = x[n]$
Scaling: $y[n] = 2\, x[n]$
Offset: $y[n] = x[n]+2$
Square signal: $y[n] = (x[n])^2$
Shift: $y[n] = x[n+m]\quad m\in Z$
\]
Decimate: $y[n] = x[2n]$
Square time: $y[n] = x[n^2]$
Moving average (combines shift, sum, scale): $y[n] = \frac{1}{2}(x[n]+x[n-1])$
Recursive average: $y[n] = x[n]+ \alpha\,y[n-1]$
So systems take input signals and produce output signals. We have seen some examples of systems, and have also introduced a broad categorization of systems as either operating on finite or infinite length signals.
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
