Podcasts about fourier series

Episode: 1878 Fourier, Egypt, and modern applied mathematics.  Today, Joseph Fourier.

Fourier Series expansion (-pi,pi) (-l,l)

Today's lecture discusses an application of Fourier series, exploring how the vocal tract filters frequencies generated by the vocal cords. Speech synthesis and recognition technology uses frequency analysis to accurately reconstruct vowels.

This lecture introduces the Fourier series representation of sequences and describes how to determine the Fourier series coefficients. It also discusses properties of Fourier series.

Deals with the details of calculating Fourier series coefficients for a function.

Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coefficients.

Introduces the idea of half-range Fourier series and addresses the question of why we use them.

Simple demonstration of how to obtain a series to evaluate approximations to pi, using a specific and quite simple Fourier series.

Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coefficients.

A Fourier series separates a periodic function into a combination (infinite) of all cosine and since basis functions.

Even functions use only cosines and odd functions use only sines. The coefficients in the Fourier series come from integrals.

Around every circle, the solution to Laplace’s equation is a Fourier series with coefficients proportional to r^n. On the boundary circle, the given boundary values determine those coefficients.

A teaching assistant works through a problem on manipulating Fourier series.

A teaching assistant works through a problem on computing Fourier series.

This video lecture discusses continuous-time Fourier serires, and the response of continuous-time LTI systems to complex exponentials. Also covered: the eigenfunction property.

This lecture will discuss the similarities and differences with discrete-time and continuous-time Fourier series. Analysis and synthesis equations, and approximation of periodic and aperiodic signals.

A proof of Parseval's theorem for trigonometric Fourier series is outlined.

The complex Fourier coefficients are calculated for the function e^t with period 2 pi.

Parseval's theorem is used to achieve a bonus result for the sum of the series of reciprocal fourth powers of odd integers.

Further use of Fourier series to find the sum of a series involving alternating signed reciprocals of odd integers.

Starting with a known Fourier series, we derive results of sumes of series involving reciprocals of powers of the whole numbers.

Fourier coefficients are evaluated for a piecewise function consisting partly of sin(t) and partly the constant 0.

Integrals whose integrand consists of products of sin and cos with themselves or each other are evaluated.

A vertical shift is applied to a function before finding its Fourier series. This reduces the work in finding the Fourier coefficients.

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range sine series for a linear f(t).

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper.

Throughout this course (and in many areas of mathematical physics) it is extremely convenient to write one function of interest as a weighted superposition of another set of functions whose behavior we are familiar with. If our system is linear, we can then analyze the behavior of the system on our function of interest by breaking it up into its components parts and adding up the results. This is the basis of functional analysis which is closely related to linear algebra. For that reason, many geometrical concepts can be leveraged in functional analysis to help understand what’s going on.

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations. This study unit is just one of many that can be found on LearningSpace, part of OpenLearn, a collection of open educational resources from The Open University. Published in ePub 2.0.1 format, some feature such as audio, video and linked PDF are not supported by all ePub readers.

Huybrechs, D (K.U. Leuven, BE) Monday 13 September 2010, 11:30-12:30

A short introduction to this album.

Transcript -- A short introduction to this album.

A short introduction to this album.

Transcript -- A short introduction to this album.

A comparison between the waveforms produced from a single note on both the flute and violin.

Transcript -- A comparison between the waveforms produced from a single note on both the flute and violin.

A comparison between the waveforms produced from a single note on both the flute and violin.

Transcript -- A comparison between the waveforms produced from a single note on both the flute and violin.

Fourier Series are introduced and are generalized to the Fourier sine and cosine tansform