How to Interpolate in the Time-Domain by Zero-Padding in the Frequency Domain | dspGuru.com
by Rick Lyons Performing interpolation on a sequence of time-domain samples is an important (often used) process in DSP, and there are many descriptions of time-domain interpolation (a kind of curve fitting) in the literature and on the Internet. However, there’s a lesser-known scheme used for interpolation that employs the inverse discrete Fourier transform (IDFT). One of the fundamental principles of discrete signals is that "zero padding" in one domain results in an increased sampling rate in the other domain. Figure 1 If, on the other hand, we zero pad (append) 96 zero-valued samples to the end of w(n), we’ll have the 128-sample w’(n) sequence shown in Figure 1(c). For each sample in Figure 1(b), we have four samples in Figure 1(d). Many folk call this process "spectral interpolation". OK, that’s time-domain zero padding. x(n)=sin(2·pi·1000·nts) + 0.5sin(2·pi·2000·nts + 3·pi/4), where ts is the sample period (1/fs), and the fs sample rate is 8000 samples/second. Figure 2 Figure 3 Figure 4

Beamforming
Beamforming is a general signal processing technique used to control the directionality of the reception or transmission of a signal on a transducer array. Using beamforming you can direct the majority of signal energy you transmit from a group of transducers (like audio speakers or radio antennae) in a chosen angular direction. Or you can calibrate your group of transducers when receiving signals such that you predominently receive from a chosen angular direction. The basic point in beamforming is, when you set multiple transducers next to each other sending out signals, you're going to get some kind of interference pattern, just like you see in a pond when you throw several stones in at once and create interfering ripples. The sin waves below are moving out from all the sources just like ripples do in a pond, and I'm going to assign variables to my arrangement rather than numbers, so that I can change them and see how those changes affect my overall resulting interference pattern.

Time period frequency formula cycle duration periodic time period to frequency wavelength calculation calculate calculator Hz hertz to ms T to f worksheet definition
● Frequencyformula − Conversion and calculation ●Period, cycle duration, periodic time, timeT to frequencyf,and frequency f to cycle duration or period T ● T = 1 / f and f = 1 / T− hertz to milliseconds and frequency to angular frequency The only kind of periods meant by people who use this phrase are periods of time, so it's a redundancy. Simply say "time" or "period." <table><tr><td bgcolor="#0000FF"><span><b>The used browser does not support JavaScript.<br />You will see the program but the function will not work. Fill out the gray box above and click at the calculation bar of the respective column. Frequency means oscillations (cycles) per second in Hz = hertz = 1/s. 1 second = 1000 ms and 1 ms = 0.001 seconds. 1 hertz = 1 Hz = cps = cycles per second. Oszilloscope: Input of the boxes (Div.) and timebase (Y) give the frequency. Formula for period (cycle duration) T Time conversion - As time goes by Formulas and equations for frequency and wavelength c = λ × f λ = c / f = c × T f = c / λ

Fun with Java, Understanding the Fast Fourier Transform (FFT) Algorithm
Java Programming, Notes # 1486 Preface Programming in Java doesn't have to be dull and boring. In fact, it's possible to have a lot of fun while programming in Java. Viewing tip You may find it useful to open another copy of this lesson in a separate browser window. Supplementary material I recommend that you also study the other lessons in my extensive collection of online Java tutorials. General Discussion The purpose of this lesson is to help you to understand how the Fast Fourier Transform (FFT) algorithm works. There are several different FFT algorithms in common use. A general-purpose transform The Fourier transform is most commonly associated with its use in transforming time-domain data into frequency-domain data. Transforming from space domain to wave number domain For example, my first job after earning a BSEE degree in 1962 was in the Seismic Research Department of Texas Instruments. Two-dimensional Fourier transforms Wave-number response to seismic waves Fourier transform images

DSP - An open source C# Complex Number and FFT library for Microsoft .NET
Exocortex.DSP An open source C# Complex Number and FFT library for Microsoft .NET 2. Demos 4. Releases All source files, Visual Studio .NET 2003 project files, binaries, XML documentation and demos are included in one package. 5. Other contributors are welcome. 6. 7. March 8, 2002 - Initial Release March 20, 2002 - Added the 2 demo applications March 22, 2002 - Added ComplexStats class March 27, 2002 - Updated webpage design May 4, 2002 - Fixed a bug in the division operator in both Complex.cs and ComplexF.cs -- the complex component of the result was being calculated incorrectly.