The above graph shows the battery voltage measured with a WiFi module connected to it. The dips are seen when the WiFi module draws peak currents during the transmit cycle. The battery used is already depleted and hence shows higher drop due to larger internal resistance. Notice how the battery voltage recovers after some time (chart below) when the current is reduced to few micro amps in sleep mode. This is due to the battery chemistry recovering after the peak currents alter the battery state. Using this information, one can easily model the battery for memory effects, internal resistance etc. Peak profile information would also help in deciding the right value of capacitor to add to the circuit to provide surge current. Too low a value can cause pre-mature battery failure and too high a value will add cost and leakage current. The right balance of capacitance can be critical to a long battery life.