Signals

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Basic signals

In the analysis of communication system, standard test signals play very important role. Such signals are used to check the performance of the system. Applying such signals at the system; the output is checked. Now depending on the input-output characteristic of that particular system; study of different properties of a system can be done. Some standard test signals are as follows:

  • Delta or unit impulse function
  • Unit step signal
  • Unit ramp signal
  • Exponential signal
  • Sinusoidal signal

Delta or unit impulse function:

  • A discrete time unit impulse function is denoted by d(n). Its amplitude is 1 at n=0 and for all other values of n; its amplitude is zero.

In the sequence form it can be represented as,

The graphical representation of delta function for D.T. signal is as shown in figure below:

Unit impulse function

  • A continuous time delta function is denoted by d(t). mathematically it is expressed as follows:

The graphical representation of delta function for C.T. signal is shown in figure below:

Unit impulse function

Unit step signal:

Unit step signal means the signal has unit amplitude for positive axis and has zero amplitude for negative axis.

There are two types of unit step signal as follows:

1) Discrete time unit step signal

2) Continuous time unit step signal

Let us discuss these two types one by one:

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1) Discrete time unit step signal

  • A discrete time unit step signal is denoted by u(n). its value is unity (1) for all positive values of n. that means its value is one for n = 0. While for other values of n, its value is zero.

2) Continuous time unit step signal

  • A continuous type unit step signal is denoted by u(t). mathematically it can be expressed as,

Unit ramp signal:

  • A discrete time unit ramp signal is denoted by ur(n). its value increases linearly with sample number n. mathematically it is defined as,

unit ramp signal

  • A continuous time ramp type signal is denoted by r(t). mathematically it is expressed as,

unit ramp signal

Exponential signal:

In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative.

A discrete time exponential signal is expressed as,

Here ‘a’ is some real constant.

If ‘a’ is the complex number then x(n) is written as,

Here ? denotes the phase. Now depending upon value of ? we have different cases:

case 1) : when a>1

Since the signal is exponentially growing; it is called rising exponential signal.

Since the signal is exponentially decreases; it is called decaying exponential signal.

4 Types of Trading Signals

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Quantified trading signals can be based on different types of strategies. Some buy high in the hopes of selling higher, while others try to create a great risk/reward ratio by buying low hoping to sell on rebounds or reversals in price action. Here are four different types of trading signals.

  1. Momentum signals are based on buying strength. Momentum traders wait for a strong move in a stock and then buy and get on-board for a short amount of time. Momentum traders usually trade short time frames of days. These work primarily in bull markets.
  2. Breakout signals are based on buying all-time highs or 52 week highs, trying to buy high and sell higher. Breakouts are bought trying to catch a parabolic move where a stock could double or even triple over weeks and months. These work primarily in strong bull markets when indexes break to all-time highs.
  3. Buying oversold dips are based on buying a long term price support level or an oversold oscillator like the 30 RSI, a price extension far from the 10 day EMA, or a -80 to -100 $NYMO. This signal tries to create a great risk/reward ratio based on buying a deep dip of a historical price range. These work best in range-bound markets.
  4. Trend following signals try to go in the direction of the long term trend by using long term moving averages like the 200 day SMA breaks as buy or sell signals, or all-time highs or lows to enter longs or shorts. These work in trends with higher highs or lower lows.

What is the importance of signals and systems ?

The Signals and systems helps to predict with some certainty,behaviour of some system when they are subjected to different input signals. It also helps to design electrical circuits or algorithms that will operate on signals to get the desired output.

In Electrical engineering programs, a class and field of study known as “signals and systems” is often seen as the “cut class” for EE careers, and is dreaded by some students as such. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous linear algebra and differential equation classes they have taken.

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