![DEFINITION
• Consider a real value function
s(x)that is integrable on an interval
of length p.
X€[0,1]and p=1
• The analysis process determines
the weight indexed by integer n.](https://image.slidesharecdn.com/fourierseries-p-230515072230-fd0e2381/85/Fourier-series-P-Ruby-Stella-Mary-pptx-3-320.jpg)
![CONVOLUTIO
THEOREMS
•The first convolution therom states
that if f and g are in <‘([-Π,Π]).
•The fouries series coefficients of the
2Π periodic convolution of f and g.](https://image.slidesharecdn.com/fourierseries-p-230515072230-fd0e2381/85/Fourier-series-P-Ruby-Stella-Mary-pptx-11-320.jpg)
Fourier series-P.Ruby Stella Mary.pptx
- 2. FOURIER SERIES • The discrete time fourier transform in fourier series. • The process of deriving the weight that describe a given function is a from of fouries series. • The analysis and synthesis anlogies are fouries transform and inverse transform.
- 3. DEFINITION • Consider a real value function s(x)that is integrable on an interval of length p. X€[0,1]and p=1 • The analysis process determines the weight indexed by integer n.
- 4. COMPLEX VALUED FUNCTION •The complex value function of a real varaible x both componets are real valued function that can be represented by a fouries series. •The two sets of coefficients and the partica sum.
- 5. CONVERGENCE •The fourier series is generally presumed to converge everywhere except at discntinuities. •The fouries series converges to the function at almost every point. •The dirichlet’s condition for fourier series the convergence of fourier series.
- 6. RIEMANN LEBESQU LEMMA •If F is integrable. •There are four riemann lebesqu lemma the imaginary parts a complex function. •This result is known as the riemann lebesgue lemma.
- 7. SYMMETRY PROPERTIES • The real and imaginary parts of a complex function are demposed into their even and odd parts. • There are four components denote the subscripts RE,RO,IE and IO. Time domain f=f RE f=f RE
- 8. DERIVATIVE PROPERTY .The fouries coefficients ^f’(n) of the derivative f’ can be expressed in terms of the fourier coefficients ^f(n) of the function f. •The fourier coefficient converge to zero.
- 11. CONVOLUTIO THEOREMS •The first convolution therom states that if f and g are in <‘([-Π,Π]). •The fouries series coefficients of the 2Π periodic convolution of f and g.
- 12. COMPACT GROUPS •The fouries series on any compact group it include those classical groups that are compact. •The four transform carries convolutions to pointwise products. •An alternative extension tocompact is the peter way theirs.
- 13. RIEMANNIAN MANIFOLDS •X is a compact riemannian manifold it has a laplace beltrami operator. •The differential operator that corresponds to palace operator the riemannian mainfold x. •Then analogy one can equation x.
- 15. •LOCALLY COMPACT ABLIAN GROUPS •The generalization to compact groups discussed above does to noncompact. •If G is compact one also obtains of fouries series.
- 16. THANK YOU