# Tag Info

Accepted

### Discrete State Space Model - Why Are We Calculating $x \left[ k + 1 \right]$ Instead of $\dot{\boldsymbol{x}} \left( t \right)$?

I will ask you something that will give you intuition. How would you calculate the Gradient of an image? Image is a discretization of reality, so how would you estimate the gradient of the "Reality" ...
• 19.6k
Accepted

### Causal Noise Free 1st Order Derivative in Discrete Domain

If there was no noise in the input, then the causal filter: $$y[k] = \frac{\frac{3}{2}x[k] - 2x[k-1] + \frac{1}{2}x[k-2]}{T_s}$$ would give the asymptotically optimal 3-sample linear approximation ...
• 13.5k

### Discrete State Space Model - Why Are We Calculating $x \left[ k + 1 \right]$ Instead of $\dot{\boldsymbol{x}} \left( t \right)$?

Hi: I've been wondering about the same exact thing myself and the light bulb finally turned on a few days ago when I went back to Kalman's 1960 paper. ( I've read it many times but not recently ). ...
• 1,117
Accepted

### Multiplying the imaginary part of DFT with a linear ramp to get a derivative

I've changed my mind during the answer. Instead of using frequency domain processing to get the derivative signal, I will provide a more direct and clean approach to get the derivative of a signal by ...
• 28.2k

### Multiplying the imaginary part of DFT with a linear ramp to get a derivative

From your comments, it look as if you want to manually create the ramp mask, and apply it in the frequency-domain so as to achieve the result of differentiation in time-domain. Considering the ideal ...
• 28.2k
Accepted

### Understanding the resulting image matrix when differentiating image

Your interpretation is correct: directional derivation operators highlight variation in a given direction. Here, you use the $2$-point discrete derivative in the $x$-direction (along image rows). It ...
• 31.9k

• 44.7k
1 vote

• 2,610
1 vote

### Time invariance and linearity of recursive system

The system is both linear and time-invariant. Theory says linearity means that for an input $$ax_1[n] + bx_2[n]$$ your output would be $$ay_1[n] + by_2[n]$$ where $y_1[n], y_2[n]$ are the outputs of ...
• 1,087
1 vote

### Linear Difference Equation and Method of Least Squares

The notation $\hat{y} \left( k \mid k - 1 \right)$ usually means this is an estimated value of $y \left( k \right)$ given all the available data up to time index $k - 1$. So generally speaking, ...
• 19.6k
1 vote

### Frequency response of numerical differentiation by polynomial interpolation / finite difference

For finite differences, as suggested by Andy, you can use MATLAB/Octave's freqz, but with some tricks to get the phase frequency response right. I'm using Wikipedia'...
• 13.5k
1 vote

### Using Parks-Mcclellan (or others) for FIR differentiator?

There is no fundamental difference between the design of standard frequency selective filters (such as low pass, high pass, etc.) and differentiators. The only difference is that for a (linear phase) ...
• 90k
1 vote

### Given a Horizontal Derivative Kernel What Would Be the Output Image?

The solution provided is correct. Here is why. To compute the derivative at index(3,5) d(3,5) = value_at(4,5) - value_at(2,5) d(3,5) = 150 - 0 d(3,5) = 150 ...
• 241

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