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
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
