Consider a continuous-time system whose output y(t) relates to the input x(t) according to the equation

y(t) = cos(a[t-b])[x(t-c)+d]

where the parameters a,b,c,d are real constants.

In the question below only focus on the parameter or parameters that are relevant to the particular property you are being asked about in the particular question.

If you need to constrain a parameter to satisfy the stated criterion, give the least restritive constraint i.e. if the system has a particular property for a range of values, be sure to specify the whole range. If no constraints are needed at all write 'none'.

a) Describe how the parameters must be constrained to make the system linear.

b) Describe how the parameters must be constrained to make the system time invariant.

c) Describe how the parameters must be constrained to make the system causal.