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Can a discrete sinusoid be a periodic signal?
Discrete sinusoids can be non-periodic even if they result from uniformly sampling a periodic continuous-time sinusoid. Consider the discrete-time signal x [ n] = cos. . ( n + π / 4), − ∞ < n < ∞, which is obtained by sampling the analog sinusoid x ( t) = cos.
Which is a solution to the discrete sinusoid problem?
Solution: The sampled signal x[n] = x(t) | t = nTs = cos(n + π / 4) has a discrete frequency ω = 1 (rad) which cannot be expressed as 2πm / N for any integers m and N because π is an irrational number. So x[n] is not periodic.
Who is the professor of discrete time sinusoids?
Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids20 / 23 Discrete-Time Sinusoids -3 -10 1 3 4 5 -2 2 6 -3 -1 0 1 3 4 5 -2 2 6 Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids21 / 23 Discrete-Time Sinusoids -3 -10 1 3 4 5 -2 2 6 -3 -1 0 1 3 4 5 -2 2 6
Which is the most used among the two sinusoids?
•Both sine and cosine trigonometric functions are collectively known as sinusoids What is the most used among the two? •Cosine Why? •Cosine is an even function (Provides considerable mathematical advantage), moreover sine is a 90o
Which is the formula for a discrete sinusoid?
Thus Ts = 2kπ / N ≤ π satisfies the Nyquist sampling condition at the same time that ensures the periodicity of the sampled signal. For instance, if we wish to have a discrete sinusoid with fundamental period N = 10, then Ts = kπ / 5, for k chosen so that the Nyquist sampling rate condition is satisfied, i.e.,
How is numerical differentiation used in signal processing?
The numerical differentiation of digitized signals is an application of this concept that has many uses in analytical signal processing.
How is a sinusoid converted to a digital signal?
The conversion of an analog signal into a digital signal consists of three steps: sampling, quantization, and coding. These are the three operations an ADC does. To illustrate them consider a sinusoid x ( t) = 4 cos (2 πt ).