Signal Homework Help

The signal can be defined as anything that tells u something about some property. Like

Motion-i.e. change of position w.r.t time

Sound-pressure variations in medium w.r.t time etc. These are 2 very popular examples and u can observe which property we are observing.

MATHEMATICAL REPRESENTATION OF A SIGNAL

Signal can be mathematically represented by a dependent variable and independent variable.

Example: x(t) = t(square) + 1

Also a signal a could be represented by sinusoidal wave .eg.x(t)=A sin (2pift+thita).

The parameters of the signal are:

1. Amplitude
2. phase
3. frequency

It is a very interesting subject because most of the problems are based on numerical analysis and derivations and complex calculations and a very less theory. Even more interesting is when you get into the deep of the creation of algorithms for coding and decoding information.

Basically, you will learn signal and systems as follow,

1. Fundamentals of Signals and Systems, which includes the classification, various operations, and properties.
2. Some techniques such as Linear-Time Invariant (LTI) system, convolution, Power spectral density and Analog to Digital conversion procedure, Digital to Analog Conversion and various errors related to them as both procedures are not able to produce exact original signal back.
3. This part equips learners with certain tools that will be useful for analysis (both Signals and Systems) and later design of systems in the subsequent semester in subjects called Digital Signal Processing, Communication System, and even Linear IC Design using Op-Amps. These tools are nothing but mathematically they are referred to as transforms. Again transforms in layman's language just change the form of mathematical quantity such that its analysis becomes easy. Think, Prism transforms white light into a spectrum of 7 colors, vice-versa. Similarly, these transforms convert,
   1. Integral or differential equations (Non-linear functions) to linear equations via Laplace Transform (For Analog/Continuous Time). Z-transform does the same thing but for the discrete-time domain.
   2. Conversion from the time domain to the frequency domain as Information is mostly in frequency plus the design of Systems is dependent mostly on frequency. Fourier Series (for periodic Signal) and Fourier Transform (FT) (for Aperiodic signal and Systems) to convert from continuous-time domain to frequency domain. Similarly, Digital Fourier Transform (DFT) or Discrete-Time Fourier Transform (DTFT) for Discrete signal and system. Fast Fourier Transform (FFT) is a technique to implement DTFT in the physical domain (using electronics) faster way. Also, the concept of convolution becomes simple multiplication here.
4. The relationship between a signal’s bandwidth and its duration, and use that relationship to predict and explain the bandwidth requirements, design of Digital Systems, and determine Stability.

Applications of signals and systems:

The signal is a detectable physical quantity by which information can be transmitted. The system is the one that processes the signal to give an output. By learning signals and systems we will have an idea of different types of signals and how a system produces an output. We can clearly get an idea about what happens inside a system. This can also be a help for learning digital image processing, digital signal processing, audio signal processing, etc.(basically we can get a clear idea about signal processing).

These are the few advantages of signals and systems in our daily life.

• SS (signals And systems ) plays a key role in communication.
• It is used for data transformation.
• It is also used for industrial automation.
• Signal processing is a highly used technique nowadays.
• Biological signal analysis brought a very new shape to our medical field.
• Sensors also work because of SS.
• Biometric( speech recognization, Fingerprints recognization, iris recognization).
• We can convert different types of signals depending on our needs.

What is the difference between a causal signal and a causal system?

Causal signals are the ones that are present only for t > 0. It means that they do not exist for a negative time. Practically, they only come into existence at the instant of observation. Assuming origin as the instant of observation, they exist only for t > 0. Crudely, we may also say causal signals exist in the right half of the chosen axes.

Causal systems are the ones in which the present output depends on either past input or present input. It simply means that they need some input in order to produce an output. They are practical systems as every system needs an input to produce an output. No practical system can exist in which output comes before the input is given.

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