Module 2 : Signals in Frequency Domain
Problem 1 :
 
Solution 1 
(a) 
where . Thus, we have 
                                   =        
                                                                                          
                                                                                           
                                                                                        
Therefore the new Fourier coefficients are 
                                                                    
 
 
(b)                                               =                
                                                                                    =                  
                                                                                     =                 
                                                                                     =                   
Hence the Fourier series coefficients of are given by 
                                                                                         
    

(c)                                      =                        
                                                                           =                     
                                                                           =                     
                                                                           =                     
Hence the Fourier series coefficients of are given by 
                                                                                    
 






(d)                                      =                     
                                                                       =                     
                                                                       =                     
Hence the Fourier series coefficients of are given by 
                                                                                           




(e)                                               =                             
                                                                                    =                             
                                                                                    =                                                   (1) 
Since has fundamental period T , has fundamental period . Therefore, from (1) the Fourier coefficients of are 
                                                                                                                      
                                                   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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