"ASSIGNMENT FOR DIGITAL SIGNALPROCESSINGProf. Rashmi PatilAssignment No: 1Questions: Answer the following multiple choice questions.The discrete time function defined as u(n)=n for n=0;=0 for n<0 isQ1an:a) Unit sample signalb) Unit step signalc) Unit ramp signald) None of the mentionedQ.2 The signal given by the equation8 ? ? | ? ( ? ) |- 8 is known as:a) Energy signalb) Power signalc) Work done signald) None of the mentionedQ.3A real valued signal x(n) is called as anti-symmetric if:a) x(n)=x(-n)b) x(n)=-x(-n)c) x(n)=-x(n)d) None of the mentionedQ.4 Time scaling operation is also known as:a) Down-samplingb) Up-samplingc) Samplingd) None of the mentioned Q.5 The function given by the equation x(n)=1, for n=0;=0, for n?0 isa:a) Step functionb) Ramp functionc) Triangular functiond) Impulse functionIf x(n) is a discrete-time signal, then the value of x(n) at nonQ.6integer value of ‘n’ is:a) Zerob) Positivec) Negatived) Not definedn The phase function of a discrete time signal x(n)=a , whereQ.7j? a=r.e is:a) tan(n?)b) n?-1 c) tan (n?)d) None of the mentionedx(n)*d(n-k)=?Q.8a) x(n)b) x(k)c) x(k)*d(n-k)d) x(k)*d(k)Q.9 The odd part of a signal x(t) is:a) x(t)+x(-t)b) x(t)-x(-t)c) (1/2)*(x(t)+x(-t))d) (1/2)*(x(t)-x(-t))n aT What is the condition for a signal x(n)=Br where r=e to beQ.10called as an decaying exponential signal?a) 0<r<8b) 0<r<1c) r>1d) r<0 ASSIGNMENT SOLUTIONS FOR DIGITALSIGNAL PROCESSINGProf. Rashmi PatilAnswer key to assignment No.11 cExplanation: When we plot the graph for the given function,we get a straight line passing through origin with a unitpositive slope. So, the function is called as unit ramp signal.2 aExplanation: We have used the magnitude-squared values ofx(n), so that our definition applies to complex-valued as wellas real-valued signals. If the energy of the signal is finite i.e.,0<E<8 then the given signal is known as Energy signal.3 bExplanation: According to the definition of anti-symmetricsignal, the signal x(n) should be symmetric over origin. So,for the signal x(n) to be symmetric, it should satisfy thecondition x(n)=-x(-n).4 aExplanation: If the signal x(n) was originally obtained bysampling a signal xa(t), then x(n)=xa(nT). Now,y(n)=x(2n)(say)=xa(2nT). Hence the time scaling operation isequivalent to changing the sampling rate from 1/T to 1/2T,that is to decrease the rate by a factor of 2. So, time scaling isalso called as down-sampling.5 d. Explanation: According to the definition of the impulsefunction, it is defined only at n=0 and is not definedelsewhere which is as per the signal given. 6 dExplanation: For a discrete time signal, the value of x(n)exists only at integral values of n. So, for a non- integer valueof ‘n’ the value of x(n) does not exist.7 bn j? n n jn? n Explanation:Givenx(n)=a =(r.e ) =r .e =x(n)=r .(cosn?+jsin n?)-1 -1 Phase function is tan (cosn?/sinn?)=tan (tan n?)=n?8cExplanation: The given signal is defined only when n=k bythe definition of delta function. So, x(n)*d(n-k)= x(k)*d(n-k)9 dExplanation: Let x(t)=x (t)+x (t)=x(-t)=x (-t)-x (-t)e o e o By subtracting the above two equations, we getx (t)=(1/2)*(x(t)-x(-t))o 10 bExplanation: When the value of ‘r’ lies between 0 and 1 thenthe value of x(n) goes on decreasing exponentially withincrease in value of ‘n’. So, the signal is called as decayingexponential signal "