This blog post implements an online numerical base converter, converting a list of floating point numbers from decimal to either binary or hexadecimal.
Enter (possibly floating point) decimal numbers in the text area below, one number per line - there must be no newline after the last number. You can enter either signed or unsigned numbers - to enable unsigned conversion, please check the checkbox which enables unsigned conversion (leaving this unchecked results in signed conversion). Alternatively you can load in a single column text file. Also fill in the number of unsigned integer bits and fractional bits, so that that resulting bitwidth will be (intbits + fracbits + 1), where intbits is the number of unsigned integer bits and fracbits is the number of fractional bits, for signed conversion. For unsigned conversion, the bitwidth will be (intbits + fracbits). Note that when converting to hexadecimal, if the bitwidth is not an integer multiple of 4, it will be rounded up to the nearest integer multiple of 4.
The number of integer bits and fractional bits must be set to accomodate the range of the input values.
As the decimal inputs can be floating point, you can select an appropriate rounding rule using the dropdown menu below.
There is the option of omitting the binary point, by leaving the appropriate checkbox below unchecked.
There is a final checkbox below that could come in handy for those who use VHDL (like I do, in my role as an FPGA Design Engineer). Checking this will result in a declaration of a signal type as an array of type std_logic_vector, and initialisation on declaration of a signal with the binary outputs. You can replace the strings <SIGNAL TYPE NAME> and <SIGNAL NAME> with a type name and signal name of your choice, after copying and pasting to your source code.
This blog post calculates the FIR Filter frequency response, in terms of gain (magnitude squared in linear units or dB) vs frequency, and the phase (in radians) vs frequency. The calculator takes as input the FIR filter coefficients, which can be complex.
The number of Fast Fourier Transform (FFT) bins can be specified in the appropriate textarea below - if left blank the number of FFT bins will be the filter length rounded up to the nearest integer power of 2. The user specified number of FFT bins must be greater than or equal to the filter length rounded up to the nearest integer power of 2.
Please enter the numbers in the text areas below - one number per line, for each of the Real and Imaginary input textareas (the textareas have already been filled in with some numbers for illustration purposes). There must be no new line after the last number.
Note that if the input is real only, the imaginary input textarea can be left empty (rather than having to fill it with the same number of zeros as there are real inputs, which can be a bit more cumbersome). Conversely, if the input is imaginary only, the real input textarea can be left empty (rather than having to fill it with the same number of zeros as there are imaginary inputs).
Alternatively you can choose to load a CSV file, which must be either a single column of numbers (for a real only input) or two comma-separated columns of numbers - the first line can be a comment line, starting with the character #.
There is the option of specifying a sampling frequency below - setting this to a non-zero value will result in the x-axes of the FIR response plots being set to the frequency as opposed to the frequency bin index. Leaving this field blank will result in the x-axes of the plots being set to the FFT bin index.
For plotting purposes, you can select between the following units: complex response i.e. real and imaginary, magnitude, magnitude squared and dB units, using the drop-down box below. For each bin, the dB is calculated as $10\times log_{10}(|FFT|^2)$ where $|FFT|^2$ is the magnitude squared value of the FFT for that bin.
There is a checkbox which allows you to center the zero frequency (i.e. DC component) of the spectrum. If the DC component is centred then the frequency indices that exceed half the sampling frequency will be set to negative values.
To calculate the FIR Filter response, press the button labelled "Calculate FIR Response" below - the results will populate the textarea below labelled "FIR Response", with two comma separated columns - the first column being the frequency (in bin index or Hz) and the second column being the PSD estimate (in dB or linear units). The first line of this textarea will be a comment line starting with character #, and describing the two columns. One can copy and paste the results from this textarea to a text file if so desired. In addition, graphs of the FIR filter response will be plotted.
Once you have pressed the "Calculate FIR Response" button to display the PSD, you can zoom in onto the plot. Note that there are two graphs representing the same data - the lower smaller graph is an overview graph representing the data in its entirety, while the larger graph is the main graph which will represent the zoomed in subsection. You can zoom by selecting sections from either the overview graph or the main graph. To completely undo the zooming operations, simply press the "Calculate FIR Response" button again.
If you change inputs to a smaller number of filter taps, press the calculate button twice for the results to take effect. Alternatively, you can simply reload the page, then fill in the input textareas.
Welcome to the dspfpgatools blog. In this blog I hope to create free online calculators/tools that could come in useful for Engineering, in particular for Digital Signal Processing and Digital Hardware Design.
You can navigate through this blog using a variety of means, including using the drop down menus just below the header.
So far the following tools have been implemented:-
The estimation of the Power Spectral Density (PSD) of a signal is of fundamental importance in Electrical Engineering, in particular Digital Communications.
This blog post implements a Power Spectral Density (PSD) Estimator using Welch's modification of the averaged periodogram estimate method. Some testing has been done, and the results are in agreement with those produced by GNU Octave (a free Matlab-clone). The averaged periodogram estimate method is also known as Bartlett's method.
Using Welch's method, the complex time domain data input samples are broken into contiguous (possibly overlapping) frames of size $N$, which has to be an integer power of 2 (as required for implementation of the Fast Fourier Transform (FFT)). Each of these frames is then weighted by the appropriate windowing function (see drop down menu below), and the $N$-point FFT is applied to the windowed signals within a frame. The magnitude squared of each resulting FFT bin is calculated for each frame, and time-averaged over all the frames to yield the PSD estimate.
Recall that for discrete time-domain input samples $x[n]$ for $n={0,1,2,..,N-1}$ the FFT (at bin $k$ for $k={0,1,2,..,N-1}$) is defined by equation
Please enter the numbers in the text areas below - one number per line, for each of the Real and Imaginary input textareas (the textareas have already been filled in with some numbers for illustration purposes). There must be no new line after the last number.
Note that if the input is real only, the imaginary input textarea can be left empty (rather than having to fill it with the same number of zeros as there are real inputs, which can be a bit more cumbersome). Conversely, if the input is imaginary only, the real input textarea can be left empty (rather than having to fill it with the same number of zeros as there are imaginary inputs).
Alternatively you can choose to load a CSV file, which must be either a single column of numbers (for a real only input) or two comma-separated columns of numbers - the first line can be a comment line, starting with the character #.
To set the number of FFT bins for spectral analysis, fill in the number of bins field. It is possible to have overlapping frames - to set the number of overlapping samples between adjacent frames, fill in the relevant field below. A value of 0 means that there is no overlap between adjacent frames.
There is the option of specifying a sampling frequency below - setting this to a non-zero value will result in the x-axes of the PSD plots being set to the frequency as opposed to the frequency bin index. Leaving this field blank will result in the x-axes of the plots being set to the FFT bin index.
To select the appropriate windowing function, use the drop down menu below. Furthermore, you can select between linear units and dB units, using the checkbox below. For each bin, the dB is calculated as $10\times log_{10}(|FFT|^2)$ where $|FFT|^2$ is the magnitude squared value of the FFT for that bin.
There is a second checkbox which allows you to center the zero frequency (i.e. DC component) of the spectrum. If the DC component is centred then the frequency indices that exceed half the sampling frequency will be set to negative values.
To perform the PSD, press the button labelled "Calculate PSD Estimate" below - the results will populate the textarea below labelled "Power Spectral Density", with two comma separated columns - the first column being the frequency (in bin index or Hz) and the second column being the PSD estimate (in dB or linear units). The first line of this textarea will be a comment line starting with character #, and describing the two columns. One can copy and paste the results from this textarea to a text file if so desired. In addition, graphs of the output PSD will be plotted.
Once you have pressed the "Calculate PSD Estimate" button to display the PSD, you can zoom in onto the plot. Note that there are two graphs representing the same data - the lower smaller graph is an overview graph representing the data in its entirety, while the larger graph is the main graph which will represent the zoomed in subsection. You can zoom by selecting sections from either the overview graph or the main graph. To completely undo the zooming operations, simply press the "Calculate PSD Estimate" button again.
If you change inputs to a smaller number of samples, press the calculate button twice for the results to take effect. Alternatively, you can simply reload the page, then fill in the input textareas.
