Determine (with justification) whether the following systems are (i) memoryless, (ii) causal, (iii) invertible, (iv) stable, and
1 answer:
Answer:
a.
y[n] = x[n] x[n-1] x[n+1]
(i) Memory-less - It is not memory-less because the given system is depend on past or future values.
(ii) Causal - It is non-casual because the present value of output depend on the future value of input.
(iii) Invertible - It is invertible and the inverse of the given system is
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is not time invariant because the system is multiplying with a time varying function.
b.
y[n] = cos(x[n])
(i) Memory-less - It is memory-less because the given system is not depend on past or future values.
(ii) Causal - It is casual because the present value of output does not depend on the future value of input.
(iii) Invertible - It is not invertible because two or more than two input values can generate same output values .
For example - for x[n] = 0 , y[n] = cos(0) = 1
for x[n] = 2 , y[n] = cos(2
) = 1
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is time invariant because the system is not multiplying with a time varying function.
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Answer:
Explanation:
Sample output:
BANK ACCOUT PROGRAM!
----------------------------------
Enter the old balance: 1234.50
Enter the transactions now.
Enter an F for the transaction type when you are finished.
Transaction Type (D=deposit, W=withdrawal, F=finished): D
Amount: 568.34
Transaction Type (D=deposit, W=withdrawal, F=finished): W
Amount: 25.68
Transaction Type (D=deposit, W=withdrawal, F=finished): W
Amount: 167.40
Transaction Type (D=deposit, W=withdrawal, F=finished): F
Your ending balance is $1609.76
Program is ending
Code to copy:
// include the necessary header files.
#include<stdio.h>
// Definition of the function
float withdraw(float account_balance, float withdraw_amount)
{
// Calculate the balace amount.
float balance_amount = account_balance - withdraw_amount;
// Check whether the withdraw amount
// is greater than 0 or not.
if (withdraw_amount > 0 && balance_amount >= 0)
{
// Assign value.
account_balance = balance_amount;
}
// return account_balance
return account_balance;
}
// Definition of the function deposit.
float deposit(float account_balance, float deposit_amount)
{
// Check whether the deposit amount is greater than zero
if (deposit_amount > 0)
{
// Update account balance.
account_balance = account_balance + deposit_amount;
}
// return account balance.
return account_balance;
}
int main()
{
// Declare the variables.
float account_balance;
float deposit_amount;
float withdrawl_amount;
char input;
// display the statement on console.
printf("BANK ACCOUT PROGRAM!\n");
printf("----------------------------------\n");
// prompt the user to enter the old balance.
printf("Enter the old balance: ");
// Input balance
scanf("%f", &account_balance);
// Display the statement on console.
printf("Enter the transactions now.\n");
printf("Enter an F for the transaction type when you are finished.\n");
// Start the do while loop
do
{
// prompt the user to enter transaction type.
printf("Transaction Type (D=deposit, W=withdrawal, F=finished): ");
// Input type.
scanf(" %c", &input);
// Check if the input is D
if (input == 'D')
{
// Prompt the user to input amount.
printf("Amount: ");
// input amount.
scanf("%f", &deposit_amount);
// Call to the function.
account_balance=deposit(account_balance,deposit_amount);
}
// Check if the input is W
if (input == 'W')
{
printf("Amount: ");
scanf("%f", &withdrawl_amount);
// Call to the function.
account_balance = withdraw(account_balance,withdrawl_amount);
}
// Check if the input is F
if (input == 'F')
{
// Dispplay the amount.
printf("Your ending balance is $%.2f\n", account_balance);
printf("Program is ending\n");
}
// End the while loop
} while(input != 'F');
return 0;
}
the picture uploaded below shows the program screenshot.
cheers, i hope this helps.
