discrete fourier series example

Signals and Systems 10-4 TRANSPARENCY 10 1 Example of the Fourier series coefficients for a discrete-time periodic signal Example 5 2: x[n] = 1 + sin 

Consider a periodic discrete-time signal with period N: and we obtain the Fourier series In above example the Fourier series coefficients dk were real

The discrete Fourier transform (DFT): For general, finite length signals ⇒ Used in practice with signals from experiments A periodic signal displays a pattern that  

For example, x[n] could be the nth digit in a string of binary digits being transmitted along some data bus in a computer Or it could be the maximum temperature for day number n Secondly, a discrete–time signal could arise from sampling a continuous–time signal at a discrete sequence of times

Note that (7 3) is valid for discrete-time signals as only the sample points of are considered It is seen that has frequency components at and the respective 

I The period of ?a discrete-time signal is expressed in samples Arun K Tangirala (IIT Madras) Applied Time-Series Analysis

"Т}аз and p 8Р pЖX etc 8 Figure 7 2: Example signal for DFT The magnitude of the DFT coefficients is shown below in Fig 7 3 Figure 7 3: DFT of four point 

Definition 2 1 Let f be integrable (not necessarily periodic) on the interval [−L, L] The Fourier series of f is the trigonometric series (2 1), where the coefficients 

Define the Discrete Fourier Series (DFS) expansion of periodic signals • Define the Example: take the periodic signal shown in figure 6 below It is easy to see  

values over one period, we suggest that you first determine an expression for the envelope of the Fourier series coefficients and then sample this envelope at the