Differentiation

Frequency response of numerical derivative

Frequency response of numerical derivative
  1. What is the derivative of frequency?
  2. Why does differentiation increase noise?
  3. What is the application of numerical differentiation?

What is the derivative of frequency?

The derivative of a sine wave of frequency f is a phase-shifted sine wave, or cosine wave, of the same frequency and with an amplitude that is proportional to f, as can be demonstrated in Wolfram Alpha.

Why does differentiation increase noise?

Another reason is that by differentiating, you remove the low-frequency components, so your eyes see mostly the high-frequency components giving you the impression of having more noise.

What is the application of numerical differentiation?

Differentiation is one of the most important concepts in calculus, which has been used almost everywhere in many fields of mathematics and applied mathematics. It is natural that numerical differentiation should be an important technique for the engineers.

Z-transform Transforming $G(z) = z-1$ to time-domain
Transforming $G(z) = z-1$ to time-domain
What will Z-transform convert time domain signal into?How do you convert Z-transform to Laplace transform?How do I convert from S domain to Z domain?...
Fourier Discrete Fourier transform of a 2D exponential decay
Discrete Fourier transform of a 2D exponential decay
What is 2D discrete Fourier transform?Which is a property of 2D DFT?What is the difference between DFT and DTFS? What is 2D discrete Fourier transfo...
Regularization Parameter choice rules for L1 regularization?
Parameter choice rules for L1 regularization?
How do you choose Tikhonov regularization parameter?Why does L1 regularization create sparsity? How do you choose Tikhonov regularization parameter?...