# Sketch and mathematically represent pdf of given signal

• dipo101
In summary, the conversation is about deriving the probability density function for two signals, represented as lambda functions, with different periodic and amplitude characteristics. The goal is to appropriately scale the functions so that the integral of the pdf over one period is equal to 1, and to graph the voltage and probability density on the x and y axes, respectively.
dipo101

## Homework Statement

I've been asked to sketch and mathematically represent the pdf of 2 signals:

(a) rep2T{5 rect(t/T) - rect((t-T)/T)}
(b) rep2T{2 rect(t/T) + 4Arect(2t/T)}

A(t) is the lambda function
A(t) = 1- t for 0 <= t <= 1
1+t for -1 <= t <= 0

Any help would be much appreciated!

## Homework Equations

I understand how to sketch the signals itself. However, how can I derive the pdf of the function?

## The Attempt at a Solution

The sketched signal is :
(a) 2T period form with a 5V amplitude rectangular lasting for 1T and -1V amplitude rectangular one lasting also for 1T.
(b) A 1T zero pulse, followed by a triangular waveform(amp = 4V) with a rect base( amp = 2V) [i.e waveform goes from 0V to 6V], the latter waveform lasts for 1T as well.

However, how I do I derive the pdf from this?

Usually, the pdf is a function which looks a good deal like the function itself, but integrates to 1 over the entire domain. In this case, you would want to define it over one period.
What do the current forms integrate to? How would you appropriately scale them so the integral becomes 1 over the period?

https://en.wikipedia.org/wiki/Probability_density_function

I think you want to graph voltage v on the x-axis and dp/dv on the y axis, where p is the probability that v lies between v and v + dv.
Not sure though - what is your idea of "pdf"?

## 1. What is the purpose of sketching and mathematically representing a signal?

The purpose of sketching and mathematically representing a signal is to visually and numerically understand the characteristics of the signal. This can help in analyzing and predicting the behavior of the signal in various systems or processes.

## 2. How do you sketch a signal?

To sketch a signal, you can plot the signal values against time or any other independent variable. The plot can be either hand-drawn or created using a graphing software. It is important to label the axes and provide a legend for clarity.

## 3. What information can be obtained from a sketch of a signal?

A sketch of a signal can provide information about the amplitude, frequency, and phase of the signal. It can also show the presence of any noise or disturbances in the signal. In addition, it can help identify any patterns or trends in the signal.

## 4. How is a signal mathematically represented?

A signal can be mathematically represented using equations or mathematical models that describe its behavior. This can include Fourier transforms, differential equations, or other mathematical functions that relate the signal values to time or other independent variables.

## 5. Why is it important to mathematically represent a signal?

Mathematically representing a signal can provide a more precise and quantitative understanding of the signal. It can also allow for the use of mathematical tools and techniques for analysis and prediction, which may not be possible with a simple sketch of the signal.

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