Digital signal processing - dsp

OpenStax

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Dsp00095-preface to digital signal processing - dsp

0.1 Table of contents

0.3 Legacy versus openstax presentation format

0.4 Miscellaneous

Dsp00100-periodic motion and sinusoids

1 Dsp00104-sampled time series

2 Dsp00108-averaging time series

Java1468-plotting engineering and scientific data using java

1 Java1489-plotting 3d surfaces using java

2 Java1492-plotting large quantities of data using java

Fourier analysis

Java1478-fun with java, how and why spectral analysis works

1 Java1482-spectrum analysis using java, sampling frequency, folding

1.1 Table of contents

1.3 Viewing tip

1.7 Discussion and sample code

1.8 Sampling frequency and the Nyquist folding frequency

1.9 Display sinusoids

1.10 Input parameters

1.11 The length of the two lists

1.12 Frequency value specifications

1.13 The plotting program named Graph06

1.14 Program output

1.15 Five horizontal plots

1.16 An upper frequency limit

1.17 The Nyquist folding frequency

1.18 The program output

1.19 Not so obvious ...

1.20 Unable to distinguish ...

1.21 One more example

1.22 The program output

1.23 The sinusoids are indistinguishable

1.24 Beginning of the class named Dsp029

1.25 Create array objects to hold sinusoidal data

1.26 Get the parameters

1.27 The getparameters method

1.28 Create the sinusoidal data

1.29 The end of the constructor

1.30 Plotting the sinusoidal data

1.31 Using graph06 to plot the sinusoidal data

1.32 The code for graphintfc01

1.33 What does this do?

1.34 The graphintfc01 interface methods

1.35 The getnmbr method

1.36 The methods named f1, f2, f3, f4, and f5

1.37 One plotting area per method

1.38 How does it work?

1.39 Doesn't know and doesn't care

1.40 Computed "on the fly"

1.41 Returned from an array

1.42 From a disk file, a database, the internet, etc.

1.43 The getNmbr method

1.44 The method named f1

1.45 Round from double to int

1.46 The remaining interface methods

1.47 That's it for dsp029

1.48 Using the interface named graphintfc01

1.49 The program named Graph06

1.50 Operational aspects of graph06

1.51 Spectral Analysis using a DFT Algorithm

1.52 The spectral analysis output

1.53 The format explained

1.54 The frequency axes

1.55 The horizontal units

1.56 Location of the folding frequency

1.57 A peak at the folding frequency

1.58 The frequency folding effect

1.59 Size of the peak at the folding frequency

1.60 A short fat peak at the top

1.61 Mapping the peaks to pixels

1.62 Another DFT example

1.63 Peaks merge at the folding frequency

1.64 The input parameters

1.65 A different data length

1.66 Computational frequency bounds

1.67 Frequencies are close to the folding frequency

1.68 The spectral analysis output

1.69 Peaks are symmetrical about the folding frequency

1.70 Peaks are well defined and wider than before

1.71 Peaks merge at the folding frequency

1.72 Implementing the dft algorithm

1.73 The program named Dsp028

1.74 Computes and displays the magnitude spectrum

1.75 Input parameters

1.76 Specification of sinusoidal frequencies

1.77 Example contents for dsp028.txt

1.78 Performing the spectral analysis

1.79 Will discuss the code in fragments

1.80 Beginning of the class named Dsp028

1.81 Declare array variables

1.82 Always processes five sinusoids

1.83 Create the raw sinusoidal data

1.84 Perform the spectral analysis

1.85 The spectral magnitude results

1.86 The end of the constructor

1.87 The getparameters method

1.88 The interface methods

1.89 The program named Graph03

1.90 The transform method of the ForwardRealToComplex01 class

1.91 Will discuss in fragments

1.92 A brief description

1.93 What does this really mean?

1.94 Compute the complex energy at each frequency

1.95 Nested for loops

1.96 Description of the transform method

1.97 The return values

1.98 The transform method parameters

1.99 Frequency increment, magnitude spectrum, and number of returned values

1.100 The beginning of the transform method

1.101 The remainder of the method and the class

1.102 Store results in output array objects

1.103 Now you know about the dft algorithm

1.104 Spectral analysis using an FFT algorithm

1.105 The program named Dsp030

1.106 Description of the program named dsp030

1.107 The input parameters

1.108 Restrictions on the data length

1.109 The sinusoidal frequency values

1.110 The plotting program

1.111 The transform method

1.112 A sample fft spectral analysis

1.113 Nothing special here

1.114 A matching dft spectral analysis

1.115 Repeat these two experiments

1.116 The ForwardRealToComplexFFT01 class

1.117 Run the programs

1.119 What's next?

1.120 Complete program listings

1.121 Miscellaneous

2 Java1483-spectrum analysis using java, frequency resolution versus data

3 Java1484-spectrum analysis using java, complex spectrum and phase angle

4 Java1485-spectrum analysis using java, forward and inverse transforms,

5 Java1486-fun with java, understanding the fast fourier transform (fft)

6 Java1490-2d fourier transforms using java, part 1

7 Java1491-2d fourier transforms using java, part 2

7.1 Table of contents

7.3 Two separate programs

7.4 Using the class named ImgMod30

7.5 Digital signal processing (DSP)

7.6 Will use in subsequent modules

7.7 Viewing tip

7.10 General discussion

7.11 The space domain

7.12 A purely real space domain

7.14 Sample programs

7.15 The class named ImgMod30

7.16 The xform2D method

7.17 Parameters

7.18 The remainder of the xform2D method

7.19 The inverseXform2D method

7.20 Parameters

7.21 The shiftOrigin method

7.22 Two views of the same wavenumber spectrum

7.23 How the wavenumber spectrum is actually computed

7.24 Computationally sound but not visually pleasing

7.25 The wavenumber spectrum is periodic

7.26 The shiftOrigin method code

7.27 End of the ImgMod30 class

7.28 The program named ImgMod31

7.29 Command line parameters

7.30 Forward and inverse Fourier transforms

7.31 Fourteen cases

7.32 A stack of output images

7.33 Numeric output

7.34 The size of the surfaces

7.35 The quality of the transform process

7.36 Matching pairs of values

7.37 How to use the program named ImgMod31

7.38 Program code for ImgMod31

7.39 Create and save the test surface

7.40 Display the test surface

7.41 An example test surface plot

7.42 Perform the forward Fourier transform

7.43 Prepare array objects to receive the transform results

7.44 Perform the forward transform

7.45 Display unshifted amplitude spectrum

7.46 Need to shift the origin for display

7.47 Shift the origin and display the results

7.48 Example displays

7.49 Perform an inverse transform

7.50 Prepare an array object to store the results

7.51 Call the inverseXform2D method

7.52 Display the result of the inverse transform

7.53 Display some numeric results

7.54 What do we know so far?

7.55 The getSpatialData method

7.56 The code for the getSpatialData method

7.57 Code and graphic output for fourteen example cases

7.59 The output surface

7.60 The wavenumber spectrum is flat

7.61 A very small error

7.63 The code for Case 1

7.64 The visual output

7.65 The input and output surfaces match visually

7.66 The real and imaginary parts

7.68 The amplitude spectrum is ugly

7.69 A very small error

7.71 A box on the diagonal in space

7.72 What do we know?

7.73 The code for Case 2

7.74 The real and imaginary parts of the spectrum

7.75 A different plotting color scheme

7.76 The amplitude spectrum

7.77 The output surface

7.78 The overall results

7.80 Amplitude spectrum should not change

7.81 The real and imaginary parts of the spectrum may change

7.82 A hypothetical example

7.83 Amplitude spectrum is the same

7.85 Another example of sin(x)/x

7.86 Our expectations are borne out

7.88 Rotated by ninety degrees

7.89 A wider peak

7.90 The real and imaginary parts

7.91 The final output matches the input

7.93 Many weighted lines of points

7.94 Black is -1, white is +1

7.95 Symmetries on four different axes

7.96 Must be zero at the wavenumber origin

7.97 Peaks at the folding wave numbers

7.98 The real and imaginary parts

7.99 The final output

7.101 Need to change the surface plotting scale

7.102 Display fewer results

7.103 A zero frequency sine wave

7.104 The code for this case

7.105 A single point at the origin

7.106 The inverse transform output is ugly

7.107 A very small error

7.109 The graphic output for Case 8

7.111 The wavenumber spectrum

7.112 The inverse Fourier transform output

7.115 The wavenumber spectrum

7.116 The inverse Fourier transform output

7.118 The wavenumber spectrum

7.119 Inverse Fourier transform output

7.121 The wavenumber spectrum

7.122 The inverse Fourier transform output

7.123 The end of the getSpatialData method

7.124 Run the program

7.126 Complete program listings

7.127 Miscellaneous

Convolution and frequency filtering

Java1487-convolution and frequency filtering in java

1 Java1488-convolution and matched filtering in java

Adaptive processing

Java2350-adaptive filtering in java, getting started

1 Java2352-an adaptive whitening filter in java

2 Java2354-a general-purpose lms adaptive engine in java

3 Java2356-an adaptive line tracker in java

4 Java2358-adaptive identification and inverse filtering using java

5 Java2360-adaptive noise cancellation using java

6 Java2362-adaptive prediction using java

Data compression and the discrete cosine transform

Java2440 understanding the lempel-ziv data compression algorithm in

1 Java2442 understanding the huffman data compression algorithm in java

2 Java2444 understanding the discrete cosine transform in java

3 Java2446 understanding the 2d discrete cosine transform in java

4 Java2448 understanding the 2d discrete cosine transform in java, part

Recursive filtering

Source: OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38

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